%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Eberhard Kranich", %%% version = "1.13", %%% date = "26 October 2010", %%% time = "15:48:47 MDT", %%% filename = "intbib.bib", %%% address = "FB WiWi and OR (Prof. Dr. Gal) %%% FernUniversit{\"a}t Hagen %%% Postfach 940 %%% D-5800 Hagen 1 %%% Germany", %%% checksum = "60396 11917 48048 425660", %%% email = "WI805 at DHAFEU11 (EARN/Bitnet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, interior point, mathematical %%% programming", %%% license = "public domain", %%% supported = "no", %%% docstring = "This is a list of references concerning %%% interior point methods for mathematical %%% programming. %%% %%% At version 1.13, the year coverage looked %%% like this: %%% %%% 1947 ( 1) 1965 ( 0) 1983 ( 1) %%% 1948 ( 0) 1966 ( 0) 1984 ( 11) %%% 1949 ( 0) 1967 ( 2) 1985 ( 63) %%% 1950 ( 0) 1968 ( 1) 1986 ( 63) %%% 1951 ( 1) 1969 ( 1) 1987 ( 89) %%% 1952 ( 0) 1970 ( 1) 1988 (125) %%% 1953 ( 1) 1971 ( 0) 1989 (159) %%% 1954 ( 1) 1972 ( 1) 1990 (253) %%% 1955 ( 2) 1973 ( 0) 1991 (192) %%% 1956 ( 0) 1974 ( 1) 1992 ( 2) %%% 1957 ( 3) 1975 ( 0) 1993 ( 0) %%% 1960 ( 0) 1978 ( 1) 1996 ( 0) %%% 1961 ( 2) 1979 ( 1) 1997 ( 0) %%% 1962 ( 0) 1980 ( 0) 1998 ( 1) %%% 1963 ( 0) 1981 ( 1) %%% 1964 ( 0) 1982 ( 1) %%% %%% Article: 304 %%% Book: 15 %%% InBook: 16 %%% InCollection: 76 %%% InProceedings: 6 %%% MastersThesis: 5 %%% Misc: 5 %%% PhdThesis: 16 %%% TechReport: 550 %%% %%% Total entries: 993 %%% %%% The user is kindly requested to send %%% corrections and/or additions to this %%% current bibliography to the forementioned %%% address. This concerns especially to talks %%% based on an existing, but not listed %%% technical report. %%% %%% First of all, the author is deeply indebted %%% to Irv Lustig, Princeton. His salient %%% encouragement and cooperation have %%% influenced the development and publication %%% of this bibliography. %%% %%% Based on Lustig's idea ``to indicate that %%% something is a talk'' (because, sometimes, a %%% talk and the corresponding report differs %%% only in title) the author has rewritten his %%% Discussion Paper published at the %%% FernUniversit{\"a}t Hagen, May 1991. A list %%% of crossreferences between talks and reports %%% will be soon published, I hope. %%% %%% Many thanks to Dick den Hertog, PhD-student %%% at the TU Delft (The Netherlands), for %%% sending his own reference list which is now %%% incorporated into this bibliography. %%% %%% At last, the author is obliged to Eric %%% Grosse and Dave Gay for making this %%% bibliography available via NETLIB. %%% %%% Current number of references : 993 %%% %%% Last edit : January 19, 1992 %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @InCollection{int:Abhyankar1, author = "S. S. Abhyankar and T. L. Morin and T. B. Trafalis", title = "Efficient faces of polytopes~: {Interior} point algorithms, parameterization of algebraic varieties, and multiple objective optimization", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "319--341", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Adler1, author = "I. Adler", title = "A primal--dual implementation of {Karmarkar}'s algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA, USA}", year = "1985", month = nov, institution = "Operations Research Center, University of California", address = "Berkeley, CA~94720, USA", } @Article{int:Adler2, author = "I. Adler and R. D. C. Monteiro", title = "Limiting behavior of the affine scaling continuous trajectories for linear programming problems", journal = "Mathematical Programming", volume = "50", year = "1991", pages = "29--51", } @TechReport{int:Adler3, author = "I. Adler and R. D. C. Monteiro", title = "A geometric view of parametric linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler4, author = "I. Adler and G. Veiga", title = "On implementing interior point methods for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles, CA, USA}", year = "1986", month = apr, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler5, author = "I. Adler and N. K. Karmarkar and G. Veiga", title = "Implementing an interior point algorithm for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach, FL, USA}", year = "1986", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler6, author = "I. Adler and N. K. Karmarkar and M. G. C. Resende and G. Veiga", title = "Implementation of an interior point algorithm for linear programming", type = "{Technical Report}", year = "1986", institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler7, author = "I. Adler and {M. de} Carvalho and M. G. C. Resende and G. Veiga", title = "Computational performance of variants of {Karmarkar}'s algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in St. Louis, USA}", year = "1987", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler8, author = "I. Adler and {M. de} Carvalho and M. G. C. Resende and G. Veiga", title = "A {Monte--Carlo} study of variants of interior point algorithms", type = "{Technical Report}", year = "1987", institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @Article{int:Adler9, author = "I. Adler and N. K. Karmarkar and M. G. C. Resende and G. Veiga", title = "Data structures and programming techniques for the implementation of {Karmarkar}'s algorithm", journal = "ORSA Journal on Computing", volume = "1", year = "1989", pages = "84--106", } @Article{int:Adler10, author = "I. Adler and N. K. Karmarkar and M. G. C. Resende and G. Veiga", title = "An implementation of {Karmarkar}'s algorithm for linear programming", journal = "Mathematical Programming", volume = "44", year = "1989", pages = "297--335", note = "Errata in {\em Mathematical Programming}, 50:415, 1991", } @TechReport{int:Adler11, author = "I. Adler and R. D. C. Monteiro", title = "An interior point algorithm applied to a class of convex separable programming problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler12, author = "I. Adler", title = "Implementation issues of path--following algorithms for linear programming", type = "{Talk held at the EURO/TIMS Joint International Conference on Operational Research in Paris, France}", year = "1988", month = jul, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Adler13, author = "I. Adler", title = "Computational tests of the {Karmarkar} algorithm", type = "{Talk held at the SIAM Conference on Optimization in Houston, TX, USA}", year = "1987", month = may, institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @InCollection{int:Adler14, author = "I. Adler and R. D. C. Monteiro", title = "Limiting behavior of the affine scaling continuous trajectories for linear programming problems", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "189--211", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Akguel1, author = "M. Akguel", title = "A short proof of {Karmarkar}'s main result", journal = "Doga Tuerk Matematik Dergisi (= Turkish Journal of Mathematics, Ankara)", volume = "14", year = "1990", pages = "48--55", } @Article{int:Akguel2, author = "M. Akguel", title = "On the exact solution of a system of linear homogeneous equations via a projective algorithm", journal = "Arabian Journal for Science and Engineering", volume = "15", number = "4", year = "1990", pages = "753--754", } @TechReport{int:Andersen1, author = "J. Andersen and R. Levkovitz and G. Mitra and M. Tamiz", title = "Adopting interior search algorithms for the solution of {LP}s for serial, coarse grain parallel and massively parallel computers", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Dept.\ of Mathematics and Statistics, Brunel University", address = "Uxbridge, Middlesex~UB8~3PH, UK", } @TechReport{int:Andersen2, author = "J. Andersen and G. Mitra", title = "Solving the {Newton} iteration step of the interior point method on massively parallel ({SIMD}) computer", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "Dept.\ of Mathematics and Statistics, Brunel University", address = "Uxbridge, Middlesex~UB8~3PH, UK", } @Article{int:Andrusenko1, author = "S. K. Andrusenko and E. A. Nurminskii and P. I. Stetsyuk", title = "Numerical experiments in a new class of algorithms in linear programming", journal = "Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki (Moscow)", volume = "27", year = "1987", pages = "349--356", note = "Translated in~: {\em USSR Computational Mathematics and Mathematical Physics}, 27(2):18--22, 1987", } @Article{int:Angier1, author = "N. Angier", title = "Folding the perfect corner", journal = "Time Magazin", volume = "124", year = "1984", month = "December 3,", pages = "55", } @TechReport{int:Anstreicher1, author = "K. M. Anstreicher", title = "Analysis of a modified {Karmarkar}'s algorithm for linear programming", type = "{Technical Report}", number = "B\#84", year = "1985", month = aug, institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @TechReport{int:Anstreicher2, author = "K. M. Anstreicher", title = "Analysis of {Karmarkar}'s algorithm for fractional linear programming", type = "{Technical Report}", year = "1985", month = nov, institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @Article{int:Anstreicher3, author = "K. M. Anstreicher", title = "A monotonic projective algorithm for fractional linear programming", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "483--498", } @Article{int:Anstreicher4, author = "K. M. Anstreicher", title = "A strengthened acceptance criterion for approximate projections in {Karmarkar}'s algorithm", journal = "Operations Research Letters", volume = "5", year = "1986", pages = "211--214", } @TechReport{int:Anstreicher5, author = "K. M. Anstreicher", title = "On the complexity of the projective algorithm for standard form linear programming", type = "{Technical Report}", year = "1987", institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @InCollection{int:Anstreicher6, author = "K. M. Anstreicher", title = "Dual ellipsoids and degeneracy in the projective algorithm for linear programming", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "141--149", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Anstreicher7, author = "K. M. Anstreicher", title = "Linear programming and the {Newton} barrier flow", journal = "Mathematical Programming", volume = "41", year = "1988", pages = "367--373", } @Article{int:Anstreicher8, author = "K. M. Anstreicher", title = "On the performance of {Karmarkar}'s algorithm over a sequence of iterations", journal = "SIAM Journal on Computing", volume = "1", number = "1", year = "1991", pages = "22--29", } @Article{int:Anstreicher9, author = "K. M. Anstreicher", title = "The worst--case step in {Karmarkar}'s algorithm", journal = "Mathematics of Operations Research", volume = "14", year = "1989", pages = "294--302", } @Article{int:Anstreicher10, author = "K. M. Anstreicher", title = "Progress in interior point algorithms since 1984", journal = "SIAM News", volume = "22", year = "1989", month = mar, pages = "12--14", } @TechReport{int:Anstreicher11, author = "K. M. Anstreicher", title = "A combined phase~{I} -- phase~{II} scaled potential algorithm for linear programming", type = "CORE Discussion Paper", number = "8939", year = "1989", institution = "Center for Operations Research and Econometrics, Universite Catholique de Louvain", address = "B-1348~Louvain-la-Neuve, Belgium", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @Article{int:Anstreicher12, author = "K. M. Anstreicher", title = "A standard form variant and safeguarded linesearch for the modified {Karmarkar} algorithm", journal = "Mathematical Programming", volume = "47", year = "1990", pages = "337--351", } @TechReport{int:Anstreicher13, author = "K. M. Anstreicher and R. A. Bosch", title = "Long steps in a ${O(n^{3}L)}$ algorithm for linear programming", type = "{Technical Report}", year = "1988", institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @TechReport{int:Anstreicher14, author = "K. M. Anstreicher and P. Watteyne", title = "A family of search directions for {Karmarkar}'s algorithm", type = "CORE Discussion Paper", number = "9030", year = "1990", institution = "Center for Operations Research and Econometrics, Universite Catholique de Louvain", address = "B-1348~Louvain-la-Neuve, Belgium", } @TechReport{int:Anstreicher15, author = "K. M. Anstreicher and {D. den} Hertog and C. Roos and T. Terlaky", title = "A long step barrier method for convex quadratic programming", type = "{Technical Report}", number = "90--53", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Anstreicher16, author = "K. M. Anstreicher", title = "Strict monotonicity and improved complexity in the standard form projective algorithm for linear programming", type = "CORE Discussion Paper", number = "9035", year = "1990", institution = "Center for Operations Research and Econometrics, Universite Catholique de Louvain", address = "B-1348~Louvain-la-Neuve, Belgium", } @Article{int:Anstreicher17, author = "K. M. Anstreicher", title = "On monotonicity in the scaled potential algorithm for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "223--232", } @Article{int:Anstreicher18, author = "K. M. Anstreicher", title = "A combined phase~{I} -- phase~{II} projective algorithm for linear programming", journal = "Mathematical Programming", volume = "43", year = "1989", pages = "209--223", } @TechReport{int:Anstreicher19, author = "K. M. Anstreicher", title = "On long step path following and {SUMT} for linear and quadratic programming", type = "{Technical Report}", year = "1990", month = aug, institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @TechReport{int:Anstreicher20, author = "K. M. Anstreicher", title = "On interior algorithms for linear programming with no regularity assumptions", type = "{Technical Report}", year = "1991", institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @TechReport{int:Anstreicher21, author = "K. M. Anstreicher and R. A. Bosch", title = "On partial updating in a potential reduction linear programming algorithm of {Kojima, Mizuno and Yoshise}", type = "{Technical Report}", year = "1991", institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @TechReport{int:Anstreicher22, author = "K. M. Anstreicher", title = "Recent developments in algorithms for linear programming", type = "{Talk held at the Third SIAM Conference on Optimization in Boston, MA, USA}", year = "1989", month = apr, institution = "Yale School of Management, Yale University", address = "New Haven, CT~06520, USA", } @TechReport{int:Anstreicher23, author = "K. M. Anstreicher", title = "Advances in interior point methods for linear programming", type = "{Tutorial held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @Article{int:Armacost1, author = "A. Armacost and S. Mehrotra", title = "A computational comparison of the network simplex method with the dual affine scaling method", journal = "Journal of the Operational Research Society of India (Opsearch)", volume = "28", number = "1", year = "1991", pages = "18--35", } @TechReport{int:Aronson1, author = "J. Aronson and R. Barr and R. Helgason and J. Kennington and A. Loh and H. Zaki", title = "The projective transformation algorithm by {Karmarkar}~: {A} computational experiment with assignment problems", type = "{Technical Report}", number = "85--OR--3", year = "1985", month = aug, institution = "Dept.\ of Operations Research, Southern Methodist University", address = "Dallas, TX~75275, USA", } @TechReport{int:Aronson2, author = "J. Aronson and R. Barr and R. Helgason and J. Kennington and A. Loh and H. Zaki", title = "A specialization of {Karmarkar}'s algorithm to solve network problems", type = "{Technical Report}", year = "1985", institution = "Dept.\ of Operations Research, Southern Methodist University", address = "Dallas, TX~75275, USA", } @TechReport{int:Asic1, author = "M. D. Asic and V. V. Kovacevic--Vujcic and M. D. Radosavljevic--Nikolic", title = "Behavior of {Karmarkar}'s method on degenerate problems", type = "{Technical Report}", year = "1988", institution = "Dept.\ of Mathematics, Michigan State University", address = "East Lansing, MI~48824, USA", } @Article{int:Asic2, author = "M. D. Asic and V. V. Kovacevic--Vujcic and M. D. Radosavljevic--Nikolic", title = "Asymptotic behavior of {Karmarkar}'s method for linear programming", journal = "Mathematical Programming", volume = "46", year = "1990", pages = "173--190", } @TechReport{int:Asic3, author = "M. D. Asic and V. V. Kovacevic--Vujcic and M. D. Radosavljevic--Nikolic", title = "Asymptotic behavior and numerical stability of {Karmarkar}'s method for linear programming", type = "{Technical Report}", year = "1986", institution = "University of Belgrade", address = "Belgrade, Yugoslavia", } @Article{int:Asic4, author = "M. D. Asic and V. V. Kovacevic--Vujcic", title = "An interior semi--infinite programming method", journal = "Journal of Optimization Theory and Applications", volume = "59", year = "1988", pages = "369--390", } @InCollection{int:Asic5, author = "M. D. Asic and V. V. Kovacevic--Vujcic and M. D. Radosavljevic--Nikolic", title = "A note on limiting behavior of the projective and the affine rescaling algorithms", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "151--157", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @InCollection{int:Asic6, author = "M. D. Asic and V. V. Kovacevic--Vujcic and M. D. Radosavljevic--Nikolic", title = "Karmarkar algoritam~: {Analiza} numericke stabilnosti i neke modifikacije", booktitle = "Proceedings of the 12th Yugoslav Symposium on Operations Research, Herceg--Novi, Yugoslavia, October 1985", year = "1985", pages = "33--41", note = "(In Yugoslav)", } @InCollection{int:Asic7, author = "M. D. Asic and V. V. Kovacevic--Vujcic and M. D. Radosavljevic--Nikolic", title = "Asimptotsko ponasanje {Karmarkarove} metode", booktitle = "Proceedings of the 13th Yugoslav Symposium on Operations Research, Herceg--Novi, Yugoslavia, October 1986", year = "1986", pages = "81--88", note = "(In Yugoslav)", } @Misc{int:At1, key = "AT and T Bell Laboratories", title = "{The {AT~\&~T KORBX} Linear Programming System, AT~\&~T Bell Laboratories, Holmdel, NJ~07733, USA}", year = "1988", address = "Holmdel, NJ~07733, USA", note = "Introduced at the ORSA/TIMS Joint National Meeting in Denver, CO, USA, October 1988", } @MastersThesis{int:Bach1, author = "R. Bach", title = "{{\"U}ber die Effizienz eines polynomialen Verfahrens zur L{\"o}sung von linearen Optimierungsproblemen. (About the efficiency of a polynomial method for solving linear programming problems)}", year = "1990", month = dec, school = "{Fachbereich Wirtschaftswissenschaften und Operations Research, FernUniversit{\"a}t Hagen}", address = "P. O. Box 940, D-5800 Hagen, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:52:31 1995", } @TechReport{int:Bagchi1, author = "A. Bagchi and B. Kalantari", title = "A method for computing approximate solution of the trust region problem with application to projective methods for quadratic programming", type = "{Working Paper}", year = "1988", institution = "Dept.\ of Computer Science, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Ballintijn1, author = "C. Ballintijn", title = "Implementation aspects and performance results of the dual--affine algorithm", type = "{Talk held at the 14th Conference on the Mathematics of Operations Research in Dalfsen, The Netherlands}", year = "1990", month = jan, institution = "Shell Research Center (KSLA)", address = "Amsterdam, The Netherlands", } @TechReport{int:Barle1, author = "J. Barle and J. Grad", title = "The implementation of {Karmarkar}'s algorithm using electronic spreadsheet", type = "{Talk held at the DGOR--Jahrestagung in Berlin, Germany}", year = "1988", month = sep, institution = "Ekonomska Fakulteta Borisa Kidrica, University of Ljubljana", address = "YU-61109~Ljubljana, Yugoslavia", bibdate = "Sat Dec 30 09:52:35 1995", } @TechReport{int:Barle2, author = "J. Barle and J. Grad", title = "The implementations of interior point methods for solving {LP on PC}", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Ekonomska Fakulteta Borisa Kidrica, University of Ljubljana", address = "YU-61109~Ljubljana, Yugoslavia", } @Article{int:Barnes1, author = "E. R. Barnes", title = "A variation on {Karmarkar}'s algorithm for solving linear programming problems", journal = "Mathematical Programming", volume = "36", year = "1986", pages = "174--182", } @TechReport{int:Barnes2, author = "E. R. Barnes", title = "A sparse matrix version of {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1986", institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes3, author = "E. R. Barnes", title = "A polynomial--time version of the affine scaling algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis, USA}", year = "1987", month = oct, institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes4, author = "E. R. Barnes", title = "The role of centering in interior point methods", type = "{Technical Report}", year = "1988", institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes5, author = "E. R. Barnes", title = "Phase--{I} procedures for interior point problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes6, author = "E. R. Barnes", title = "Numerical techniques for interior point methods", type = "{Technical Report}", year = "1989", institution = "School of Industrial and Systems Engineering, Georgia Institute of Technology", address = "Atlanta, GA~30322-0205, USA", } @TechReport{int:Barnes7, author = "E. R. Barnes", title = "Computing centers and minimum covering ellipsoids for polytopes", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "School of Industrial and Systems Engineering, Georgia Institute of Technology", address = "Atlanta, GA~30322-0205, USA", } @TechReport{int:Barnes8, author = "E. R. Barnes and D. J. Jensen", title = "Affine--scaling algorithms for linear programming with centering steps", type = "{Technical Report}", year = "1987", institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes9, author = "E. R. Barnes and S. Chopra and D. J. Jensen", title = "Polynomial--time convergence of the affine scaling algorithm with centering", type = "{Talk held at the Conference on Progress in Mathematical Programming, Asimolar Conference Center, Pacific Grove, CA, USA}", year = "1987", month = mar, institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes10, author = "E. R. Barnes and S. Chopra and D. J. Jensen", title = "The affine scaling method with centering", type = "{Technical Report}", year = "1988", institution = "Dept.\ of Mathematical Sciences, IBM~T.~J.~Watson Research Center", address = "P.~O.~Box~218, Yorktown Heights, NY~10598, USA", } @TechReport{int:Barnes11, author = "E. R. Barnes and S. Chopra and D. J. Jensen", title = "A polynomial--time version of the affine--scaling algorithm", type = "{Working Paper Series}", number = "88--101", year = "1988", institution = "Graduate School of Business and Administration, New York University", address = "New York, NY~10006, USA", } @TechReport{int:Barnes12, author = "E. R. Barnes and A. Moretti", title = "On the convergence of the affine scaling algorithm", type = "{Technical Report}", year = "1991", institution = "School of Industrial and Systems Engineering, Georgia Institute of Technology", address = "Atlanta, GA~30332-0205, USA", } @InCollection{int:Barnes13, author = "E. R. Barnes", title = "Some results concerning convergence of the affine scaling algorithm", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "131--139", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Barnes14, author = "E. R. Barnes", title = "Minimum containing ellipsoids and regular polyhedra", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "2--6", } @TechReport{int:Barutt1, author = "J. F. Barutt and J. A. Ludvijsen and E. M. Olsen", title = "Using the interior point method for solving large scale crew scheduling problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Northwest Airlines F-7140, MSP International Airport", address = "St.~Paul, MN~55111, USA", } @Article{int:Bayer1, author = "D. A. Bayer and J. C. Lagarias", title = "Karmarkar's linear programming algorithm and {Newton}'s method", journal = "Mathematical Programming", volume = "50", year = "1991", pages = "291--330", } @Article{int:Bayer2, author = "D. A. Bayer and J. C. Lagarias", title = "The nonlinear geometry of linear programming, {Part~I~: A}ffine and projective scaling trajectories", journal = "Transactions of the American Mathematical Society", volume = "314", number = "2", year = "1989", pages = "499--526", } @Article{int:Bayer3, author = "D. A. Bayer and J. C. Lagarias", title = "The nonlinear geometry of linear programming, {Part~II}~: {Legendre} transform coordinates", journal = "Transactions of the American Mathematical Society", volume = "314", number = "2", year = "1989", pages = "527--581", } @Misc{int:Bayer4, author = "D. A. Bayer and N. K. Karmarkar and J. C. Lagarias", title = "Methods and apparatus for optimization system operational parameters", howpublished = "U.~S.~Patent No.~4.744.027", year = "1988", note = "AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA", } @InBook{int:Bazaraa1, author = "M. S. Bazaraa and J. J. Jarvis and H. F. Sherali", title = "Linear Programming and Network Flows", chapter = "8.4~: {Karmarkar}'s projective algorithm, pages 380--394, chapter 8.5~: {Analysis} of {Karmarkar}'s algorithm", year = "1990", pages = "394--418", publisher = "John Wiley \& Sons", address = "New York, NY, USA", edition = "second", } @InBook{int:Beisel1, author = "E. P. Beisel and M. Mendel", title = "{Optimierungsmethoden des Operations Research, Band 1~% (Optimization Methods of Operations Research, Vol.~1)}", chapter = "11~: {Die Projektionsmethode von Karmarkar~(The projection method of Karmarkar)}", pages = "169--187", publisher = "Vieweg Verlag", address = "Braunschweig, Germany", year = "1987", note = "(In German)", bibdate = "Sat Dec 30 09:51:00 1995", } @TechReport{int:BenDaya1, author = "M. {Ben--Daya} and C. M. Shetty", title = "Polynomial barrier function algorithm for linear programming", type = "{Technical Report}", number = "J~88--4", year = "1988", institution = "School of Industrial and Systems Engineering, Georgia Institute of Technology", address = "Atlanta, GA~30322-0205, USA", } @Article{int:BenDaya2, author = "M. {Ben--Daya} and C. M. Shetty", title = "Polynomial barrier function algorithm for convex quadratic programming", journal = "Arabian Journal for Science and Engineering", volume = "15", number = "4", year = "1990", pages = "657--670", } @TechReport{int:Benjamin1, author = "J. Benjamin and M. Dialsy", title = "Some applications of the primal--dual interior point algorithm using {GAUSS} programming language", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Economics Department, North Carolina A~\&~T State University", address = "Greensboro, NC~27411, USA", } @Article{int:Bertsekas1, author = "D. P. Bertsekas", title = "Projected {Newton} methods for optimization problems with simple constraints", journal = "SIAM Journal on Control and Optimization", volume = "20", year = "1982", pages = "221--246", } @TechReport{int:Betke1, author = "U. Betke and P. Gritzmann", title = "Projection algorithms for linear programming", type = "{Technical Report}", year = "1986", institution = "University of Siegen", address = "H{\"o}lderlinstr.~3, D-5900~Siegen, Germany", bibdate = "Sat Dec 30 09:52:39 1995", } @TechReport{int:Birge1, author = "J. R. Birge and L. Qi", title = "Solving stochastic linear programs via a variant of {Karmarkar}'s algorithm", type = "{Technical Report}", number = "85--12", year = "1985", institution = "Dept.\ of Operations Research, University of Michigan", address = "Ann Arbor, MI~48103, USA", } @Article{int:Birge2, author = "J. R. Birge and L. Qi", title = "Computing block--angular {Karmarkar} projections with applications to stochastic programming", journal = "Management Science", volume = "34", year = "1988", pages = "1472--1479", } @TechReport{int:Birge3, author = "J. R. Birge and R. M. Freund", title = "Prior reduced fill-in in solving equations in interior point algorithm", type = "{Working Paper}", number = "OR~3186--90--MS", year = "1990", institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", bibdate = "Sat May 4 17:22:15 1996", } @TechReport{int:Birge4, author = "J. R. Birge and C. Rosa", title = "A simplified proof of the general convergence of affine scaling", type = "{Technical Report}", number = "91--7", year = "1991", institution = "Dept.\ of Operations Research, University of Michigan", address = "Ann Arbor, MI~48103, USA", } @TechReport{int:Birge5, author = "J. R. Birge and D. Holmes", title = "Using interior point methods for stochastic linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Operations Research, University of Michigan", address = "Ann Arbor, MI~48103, USA", } @TechReport{int:Bixby1, author = "R. E. Bixby and J. W. Gregory and I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "Very large--scale linear programming~: {A} case study in combining interior point and simplex methods", type = "{Technical Report}", number = "J--91--07", year = "1991", month = may, institution = "School of Industrial and Systems Engineering, Georgia Institute of Technology", address = "Atlanta, GA~30332, USA", note = "Technical Report SOR~91--08, School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University, Princeton, NJ~08544, USA, May 1991. Technical Report RRR~34--91, RUTCOR Center of Operations Research, Rutgers University, New Brunswick, NJ~08903, USA, 1991", } @Article{int:Blair1, author = "C. E. Blair", title = "The iterative step in the linear programming algorithm of {N. Karmarkar}", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "537--539", } @TechReport{int:Blair2, author = "C. E. Blair", title = "{Karmarkar}'s algorithm and the simplex algorithm", type = "{Technical Report}", year = "1989", institution = "College of Commerce and Business Administration, University of Illinois at Urbana--Champaign", address = "Urbana, IL~61820, USA", } @InCollection{int:Bloch1, author = "A. M. Bloch", title = "Steepest descent, linear programming, and {Hamiltonian} flows", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "77--88", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Blum1, author = "L. Blum", title = "Towards an asymptotic analysis of {Karmarkar}'s algorithm", journal = "Information Processing Letters", volume = "23", year = "1986", pages = "189--194", } @Article{int:Blum2, author = "L. Blum", title = "A new simple homotopy algorithm for linear programming {I}", journal = "Journal of Complexity", volume = "4", year = "1988", pages = "124--136", } @TechReport{int:Boggs1, author = "P. T. Boggs and P. D. Domich and C. Witzgall", title = "On center trajectories for linear programming", type = "{Technical Report}", year = "1988", institution = "United States Department of Commerce, National Institute of Standards and Technology, Center for Applied Mathematics", address = "Gaithersburg, MD~20899, USA", } @Article{int:Boggs2, author = "P. T. Boggs and P. D. Domich and J. R. Donaldson and C. Witzgall", title = "Algorithmic enhancements to the method of center for linear programming", journal = "ORSA Journal on Computing", volume = "1", year = "1989", pages = "159--171", } @TechReport{int:Boggs3, author = "P. T. Boggs", title = "Higher--order methods for large linear and quadratic programming problems", type = "{Talk held at the Second International Conference on Industrial and Applied Mathematics (ICIAM~'91), Washington, DC, USA}", year = "1991", month = jul, institution = "United States Department of Commerce, National Institute of Standards and Technology, Center for Applied Mathematics", address = "Gaithersburg, MD~20899, USA", } @Article{int:Boggs4, author = "P. T. Boggs", title = "Comparing algorithms is not an easy task", journal = "SIAM News", volume = "19", number = "1", year = "1986", pages = "7", } @Article{int:Boggs5, author = "P. T. Boggs and P. D. Domich and J. E. Rogers and C. Witzgall", title = "An interior--point method for linear and quadratic programming problems", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "32--40", } @TechReport{int:Borchers1, author = "B. Borchers and J. E. Mitchell", title = "Using an interior point method in a branch and bound algorithm for integer programming", type = "{RPI Mathematical Report}", number = "195", year = "1991", institution = "Dept.\ of Mathematical Sciences, Rensselaer Polytechnic Institute", address = "Troy, NY~12180-3590, USA", } @TechReport{int:Bosch1, author = "R. Bosch and K. M. Anstreicher", title = "A partial updating algorithm for linear programs with many variables and few constraints", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Mathematics, Oberlin College", address = "Oberlin, OH~44074, USA", } @Book{int:Box1, author = "M. J. Box and D. Davies and W. H. Swann", title = "Nonlinear Optimization Technique", year = "1969", series = "ICI Monograph of Mathematics and Statistics", volume = "5", publisher = "Oliver and Boyd Ltd.", address = "London, UK", } @Article{int:Bregman1, author = "L. M. Bregman", title = "A polynomial--time simplex type method for solving linear systems of inequalities", journal = "Kibernetika (Kiev)", volume = "26", number = "1", year = "1990", pages = "84--87", note = "Translated in~: {\em Cybernetics (USA)}, 26(1):106--110, 1990", } @Article{int:Brophy1, author = "J. F. Brophy and P. W. Smith", title = "Prototyping {Karmarkar}'s algorithm using {MATH/PROTRAN}", journal = "International Mathematical and Statistical Libraries (IMSL) Directions", volume = "5", year = "1988", pages = "2--3", } @InCollection{int:Brown1, author = "G. W. Brown and T. C. Koopmans", title = "Computational suggestions for maximizing a linear function subject to linear inequalities", booktitle = "Activity Analysis of Production and Allocation", publisher = "John Wiley \& Sons", address = "New York, NY, USA", editor = "T. C. Koopmans", year = "1951", pages = "377--380", } @TechReport{int:Brown2, author = "G. G. Brown and R. D. McBride and K. R. Wood", title = "Computational methods in the projective linear programming algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA, USA}", year = "1985", month = nov, institution = "Dept.\ of Operations Research, Naval Postgraduate School", address = "Monterey, CA~93943, USA", } @Article{int:Carolan1, author = "W. Carolan and J. Hill and J. Kennington and S. Niemi and S. Wichmann", title = "An empirical evaluation of the {KORBX} algorithms for military airlift applications", journal = "Operations Research", volume = "38", year = "1990", pages = "240--248", } @Article{int:Caroll1, author = "C. W. Caroll", title = "The created response surface technique for optimizing nonlinear restrained systems", journal = "Operations Research", volume = "9", number = "2", year = "1961", pages = "169--184", } @TechReport{int:Carpenter1, author = "T. J. Carpenter and I. J. Lustig and J. M. Mulvey and D. F. Shanno", title = "A primal--dual interior point method for convex separable nonlinear programs", type = "{RUTCOR Research Report}", number = "RRR~25--90", year = "1990", month = may, institution = "RUTCOR -- Rutgers Center for Operations Research, Hill Center for Mathematical Sciences", address = "New Brunswick, NJ~08903, USA", note = "Technical Report SOR~90--02, School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University, Princeton, NJ~08544, USA, 1990", } @TechReport{int:Carpenter2, author = "T. J. Carpenter and I. J. Lustig and J. M. Mulvey and D. F. Shanno", title = "Higher order predictor--corrector interior point methods with application to quadratic objectives", type = "{RUTCOR Research Report}", number = "RRR~67--90", year = "1990", institution = "RUTCOR -- Rutgers Center for Operations Research, Hill Center for Mathematical Sciences", address = "New Brunswick, NJ~08903, USA", note = "Technical Report SOR~90--09, School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University, Princeton, NJ~08544, USA, November 1990", } @TechReport{int:Cavalier1, author = "T. M. Cavalier and T. C. Schall", title = "Implementing a projective algorithm for solving inequality constrained linear programs", type = "{IMSE Working Paper}", number = "86--128", year = "1986", institution = "Dept.\ of Industrial and Management Systems Engineering, Pennsylvania State University", address = "University Park, PA~16802, USA", } @Article{int:Cavalier2, author = "T. M. Cavalier and T. C. Schall", title = "Implementing an affine scaling algorithm for linear programming", journal = "Computers and Operations Research", volume = "14", year = "1987", pages = "341--347", } @TechReport{int:Cavalier3, author = "T. M. Cavalier and A. L. Soyster", title = "Some computational experience and a modification of the {Karmarkar} algorithm", type = "{Working Paper}", number = "85--105", year = "1985", institution = "Dept.\ of Industrial and Management Systems Engineering, Pennsylvania State University", address = "University Park, PA~16802, USA", } @Article{int:Censor1, author = "Y. Censor and A. Lunt", title = "Optimization on `$log~x$' entropy over linear inequality constraints", journal = "SIAM Journal on Control and Optimization", volume = "25", year = "1987", pages = "921--933", } @TechReport{int:Chandru1, author = "V. Chandru and B. Kochar", title = "A class of algorithms for linear programming", type = "{Research Memorandum}", number = "85--14", year = "1985", institution = "Dept.\ of Industrial Engineering, Purdue University", address = "West Lafayette, IN~47907, USA", note = "Revised 1986", } @TechReport{int:Chandru2, author = "V. Chandru and B. Kochar", title = "Exploiting special structures using a variant of {Karmarkar}'s algorithm", type = "{Research Memorandum}", number = "86--10", year = "1986", institution = "Dept.\ of Industrial Engineering, Purdue University", address = "West Lafayette, IN~47907, USA", } @TechReport{int:Chandru3, author = "V. Chandru", title = "Notes on {Karmarkar}'s new algorithm for linear programming", type = "{Unpublished Memorandum}", year = "1984", institution = "Dept.\ of Industrial Engineering, Purdue University", address = "West Lafayette, IN~47907, USA", } @Article{int:Chang1, author = "S. Y. Chang and K. G. Murty", title = "The steepest descent gravitational method for linear programming", journal = "Discrete Applied Mathematics", volume = "25", year = "1989", pages = "211--239", } @TechReport{int:Charnes1, author = "A. Charnes and T. Song and M. Wolfe", title = "An explicit solution sequence and convergence of {Karmarkar}'s algorithm", type = "{Research Report}", number = "CCS~501", year = "1984", institution = "Center for Cybernetic Studies, University of Texas", address = "Austin, TX~78712-1177, USA", } @TechReport{int:Chen1, author = "S. Chen", title = "Computational experience with the {Karmarkar} algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles, CA, USA}", year = "1986", month = apr, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Chen2, author = "S. Chen and D. N. Lee", title = "Supercomputers and an efficient implementation of {Karmarkar}'s algorithm", type = "{Talk held at the SIAM National Meeting on Numerical Analysis in Denver, CO, USA}", year = "1987", institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Cheng1, author = "Y. C. Cheng and K. T. Medhi", title = "The {AT~\&~T KORBX Linear Programming System}~: {Preconditioned} conjugate gradient implementation", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Cheng2, author = "Y. C. Cheng and J. M. Liu and M. Meketon and P. Wang and R. Vanderbei and L. Slutsman", title = "Linear programming algorithms implemented on the {AT~\&~T KORBX System}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Cheng3, author = "Y. C. Cheng and D. J. Houck and E. Housos and C. Huang and M. S. Meketon and L. Slutsman and R. Vanderbei and P. Wang", title = "The {AT~\&~T~KORBX Linear Programming System}~: {System} architecture and performance", type = "{Talk held at the 13th International Symposium on Mathematical Programming in Tokyo, Japan}", year = "1988", month = aug, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @Article{int:Cheng4, author = "Y. C. Cheng and D. J. Houck and J. M. Liu and M. S. Meketon and L. Slutsman and R. J. Vanderbei and P. Wang", title = "The {AT~\&~T~KORBX System}", journal = "AT~\&~T Technical Journal", volume = "68", year = "1989", pages = "7--19", } @TechReport{int:Chifflet1, author = "M. J. Chifflet and A. Lisser and D. Tachat and P. Tolla", title = "Computing block--angular {Karmarkar} projections with applications to multicommodity flow problems", type = "{Talk held at the 12th Triennial Conference on Operations Research in Athens, Greece}", year = "1990", month = jun, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @Article{int:Chiment1, author = "J. J. Chiment", title = "Complexity issues for numerical optimization", journal = "SIAM News", volume = "24", number = "3", year = "1991", month = may, pages = "24--25", } @TechReport{int:Chiu1, author = "S. S. Chiu and Y. Ye", title = "Recovering the shadow price in projection methods for linear programming", type = "{Technical Report}", year = "1985", institution = "Engineering Economic Systems Department, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Chiu2, author = "S. S. Chiu and Y. Ye", title = "Simplex method and {Karmarkar}'s algorithm~: {A} unifying structure", type = "{Technical Report}", year = "1985/86", institution = "Engineering Economic Systems Department, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Choi1, author = "I. C. Choi and D. Goldfarb", title = "Interior point methods for solving structured linear programs using parallel computation", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Choi2, author = "I. C. Choi and D. Goldfarb", title = "Detecting optimal basic and nonbasic variables prior to optimality in interior point methods", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Choi3, author = "I. C. Choi and C. L. Monma and D. F. Shanno", title = "Computational experience with a primal--dual interior point method for linear programming", type = "{Technical Report}", year = "1989", institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @Article{int:Choi4, author = "I. C. Choi and C. L. Monma and D. F. Shanno", title = "Further development of a primal--dual interior point method", journal = "ORSA Journal on Computing", volume = "2", year = "1990", pages = "304--311", } @InCollection{int:Choi5, author = "I. C. Choi and D. Goldfarb", title = "Solving multicommodity network flow problems by an interior point method", booktitle = "Large--Scale Numerical Optimization, Papers from the Workshop held at Cornell University, Ithaca, NY, USA, October 1989", series = "SIAM Proceedings in Applied Mathematics", volume = "46", year = "1990", pages = "58--69", editor = "T. F. Coleman and Y. Li", publisher = "Society of Industrial and Applied Mathematics (SIAM)", address = "Philadelphia, PA, USA", } @Article{int:Christiansen1, author = "E. Christiansen and K. O. Kortanek", title = "Computing material collapse displacement fields on a {Cray~X--MP/48} by the {LP} primal affine scaling algorithm", journal = "Annals of Operations Research", volume = "22", year = "1990", pages = "355--376", } @Article{int:Christiansen2, author = "E. Christiansen and K. O. Kortanek", title = "Computation of the collapse state in limit analysis using the {LP} primal affine scaling algorithm", journal = "Journal of Computational and Applied Mathematics", volume = "34", year = "1991", pages = "47--63", } @Article{int:Chu1, author = "S. C. K. Chu", title = "On the existence of positive non--extreme point solutions of linear programming", journal = "International Journal of Mathematical Education in Science and Technology", volume = "21", year = "1990", pages = "99--103", } @Article{int:Clark1, author = "C. E. Clark and J. L. Strand", title = "Application of the {Karmarkar} algorithm and expert system technology to transmission network planning", journal = "GLOBECOM Tokyo~'87~: Conference Record of the IEEE/IEICE Global Telecommunications Conference in Tokyo", volume = "2", year = "1987", pages = "270", } @Book{int:Clausen1, author = "J. Clausen and F. A. {Al--Khayyal}", title = "Interior Point Methods", year = "1991", month = aug, series = "COAL Newsletter", volume = "19", publisher = "Mathematical Programming Society", } @TechReport{int:Coleman1, author = "T. Coleman and Y. Li", title = "Quadratic interior point algorithms for piecewise linear problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @Book{int:Coleman2, author = "T. F. Coleman and Y. Li", title = "Large--Scale Optimization, Papers from the Workshop held at Cornell University, Ithaca, {NY}, {USA}, October 1989", year = "1990", series = "SIAM Proceedings in Applied Mathematics", volume = "46", publisher = "Society of Industrial and Applied Mathematics (SIAM)", address = "Philadelphia, PA, USA", } @TechReport{int:Colmenares1, author = "O. Colmenares", title = "Karmarkar's linear programming algorithm~: {Better} or worse than the classical method~?", type = "{Technical Report}", year = "1985", month = jan, institution = "Graduate School of Management, University of California at Los Angeles", address = "Los Angeles, CA, USA", } @Article{int:Conway1, author = "R. Conway and M. Magazine", title = "A case against software patents", journal = "OR/MS Today", volume = "18", number = "1", year = "1991", month = feb, pages = "14--15", } @InBook{int:Cook1, author = "T. M. Cook and R. A. Russell", title = "Introduction to Management Science", chapter = "4~: {An} alternative to the simplex method --- {Karmarkar}'s algorithm", pages = "137--139", publisher = "Prentice Hall", address = "Englewood Cliffs, NJ~07632, USA", edition = "fourth", year = "1989", } @Article{int:Cremonese1, author = "P. Cremonese", title = "Programmazione lineare e algoritmo proiettivo. {Implementazione}, experienze, relazione col simplesso {(Linear Programming and Projective Algorithm. Implementation, experiences, Simplex Relation)}", journal = "Ricerca Operativa (Italy)", volume = "18", year = "1988", pages = "73--102", note = "(In Italian)", } @TechReport{int:Dantzig1, author = "G. B. Dantzig and Y. Ye", title = "A build--up interior method for linear programming~: {Affine} scaling form", type = "{Technical Report}", number = "SOL~90--4", year = "1990", month = feb, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Dantzig2, author = "G. B. Dantzig and D. Goldfarb and E. Lawler and C. Monma and S. M. Robinson", title = "Report of the {Committee on Algorithms and the Law}", journal = "Optima (The Mathematical Programming Society Newsletter)", volume = "33", year = "1991", month = jun, pages = "2--19", note = "Containing~: B.~Kahin, The case against {"software patents"}, Appendix~A, pages 5--13, and The League for Programming Freedom, Against software patents, Appendix~B, pages 14--19", } @TechReport{int:Dantzig3, author = "G. B. Dantzig and Y. Ye", title = "A build--up interior method for linear programming~: {Affine} scaling form", type = "{Technical Report}", year = "1991", month = jul, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Dantzig4, author = "G. B. Dantzig", title = "Dikin's interior method for {LP}", type = "{Manuscript}", year = "1988", institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Dantzig5, author = "G. B. Dantzig and D. Goldfarb and E. Lawler and C. Monma and S. M. Robinson", title = "Report of the {MPS Committee on Algorithms and the Law}", journal = "SIAM News", volume = "24", number = "6", year = "1991", month = nov, pages = "3, 18", } @Article{int:David1, author = "{David~II Report}", title = "Renewing {U.S.} mathematics --- {A} plan for the 1990s, {Section}~24~: {Interior} point methods for linear programming", journal = "Notices of the American Mathematical Society", volume = "37", number = "8", year = "1990", month = oct, pages = "984--1004, esp.\ 1001--1002", bibdate = "Mon Sep 30 17:34:54 1996", } @Article{int:Dennis1, author = "J. Dennis and A. M. Morshedi and K. Turner", title = "A variable metric variant of the {Karmarkar} algorithm for linear programming", journal = "Mathematical Programming", volume = "39", year = "1987", pages = "1--20", } @InProceedings{int:Derigs1, author = "U. Derigs", title = "{Neuere Ans{\"a}tze in der Linearen Optimierung---Motivation, Konzepte und Verfahren~(Recent results in linear programming---motivation, concepts and methods)}", booktitle = "Operations Research Proceedings 1985", editor = "L. Streitfeldt and H. Hauptmann and A. W. Marusev and D. Ohse and U. Pape", year = "1986", pages = "47--58", address = "Springer-Verlag, Berlin, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:52:42 1995", } @Article{int:Diao1, author = "Z. Y. Diao", title = "Karmarkar's algorithm and its modification", journal = "Chinese Journal on Operations Research", volume = "7", number = "1", year = "1988", pages = "73--75", } @Article{int:Diao2, author = "Z. Y. Diao", title = "A remark on {Karmarkar}'s algorithm", journal = "Chinese Journal on Operations Research", volume = "7", number = "2", year = "1988", pages = "61--62", } @Article{int:Didderich1, author = "G. T. Didderich", title = "Some remarks on {Karmarkar}'s potential function", journal = "Aequationes Mathematicae", volume = "36", year = "1988", pages = "57--75", } @Article{int:Dikin1, author = "I. I. Dikin", title = "Iterative solution of problems of linear and quadratic programming", journal = "Doklady Akademii Nauk SSSR", volume = "174", year = "1967", pages = "747--748", note = "Translated in~: {\em Soviet Mathematics Doklady}, 8:674--675, 1967", } @Article{int:Dikin2, author = "I. I. Dikin", title = "On the convergence of an iterative process", journal = "Upravlyaemye Sistemi", volume = "12", year = "1974", pages = "54--60", note = "(In Russian)", } @Article{int:Dikin3, author = "I. I. Dikin", title = "Letter to the editor", journal = "Mathematical Programming", volume = "41", year = "1988", pages = "393--394", } @Article{int:Ding1, author = "J. Ding and T. Y. Li", title = "An algorithm based on weighted logarithmic barrier functions for linear complementarity problems", journal = "Arabian Journal for Science and Engineering", volume = "15", number = "4", year = "1990", pages = "769--685", } @Article{int:Ding2, author = "J. Ding and T. Y. Li", title = "A polynomial--time predictor--corrector algorithm for a class of linear complementarity problems", journal = "SIAM Journal on Computing", volume = "1", number = "1", year = "1991", pages = "83--92", } @TechReport{int:Dinn1, author = "J. Dinn", title = "A new polynomial--time algorithm for linear programming", type = "{Technical Report}", year = "1988", institution = "Dept.\ of Mathematics, Michigan State University", address = "East Lansing, MI~48824, USA", } @Article{int:Dinn2, author = "N. F. Dinn and N. K. Karmarkar and L. P. Sinha", title = "Karmarkar algorithm enables interactive planning of networks", journal = "Record AT~\&~T~Bell Laboratories", volume = "64", number = "2", year = "1986", pages = "11--13", } @Article{int:Dodani1, author = "M. H. Dodani and A. J. G. Babu", title = "Karmarkar's projective method for linear programming~: {A} computational survey", journal = "Computers and Industrial Engineering", volume = "13", year = "1987", pages = "285--289", } @Article{int:Dodani2, author = "M. H. Dodani and A. J. G. Babu", title = "Karmarkar's projective method for linear programming~: {A} computational appraisal", journal = "Computers and Industrial Engineering", volume = "16", year = "1989", pages = "198--206", } @Article{int:Dodani3, author = "M. H. Dodani and A. J. G. Babu", title = "Karmarkar's projective method for linear programming~: {A} computational survey", journal = "International Journal of Mathematical Education in Science and Technology", volume = "21", year = "1990", pages = "191--212", } @Book{int:Dolecki1, author = "S. Dolecki", title = "Optimization~: Proceedings of the 5th French--German Conference in Castel--Novel, Varetz, France, October 1988", year = "1989", series = "Lecture Notes in Mathematics", volume = "1405", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:52:45 1995", } @TechReport{int:Domich1, author = "P. D. Domich and P. T. Boggs and J. R. Donaldson and C. Witzgall", title = "Optimal 3--dimensional methods for linear programming", type = "{Technical Report}", number = "NISTIR~89--4225", year = "1989", month = dec, institution = "United States Department of Commerce, National Institute of Standards and Technology", address = "Gaithersburg, MD~20899, USA", } @Article{int:Domich2, author = "P. D. Domich and P. T. Boggs and J. E. Rogers and C. Witzgall", title = "Optimizing over 3--d subspaces in an interior point method", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "315--342", } @TechReport{int:Domich3, author = "P. D. Domich and P. T. Boggs and J. R. Donaldson and C. Witzgall", title = "Third order correction methods to the method of centers for linear programming problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "United States Department of Commerce, National Institute of Standards and Technology, Applied and Computational Mathematics Division", address = "Boulder, CO~80303, USA", } @TechReport{int:Domich4, author = "P. D. Domich and P. T. Boggs and J. R. Donaldson and C. Witzgall", title = "An interior point approach for linear and quadratic programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "United States Department of Commerce, National Institute of Standards and Technology, Applied and Computational Mathematics Division", address = "Boulder, CO~80303, USA", } @TechReport{int:Doup1, author = "T. Doup and R. Bisseling and L. Loyens", title = "A parallel interior point algorithm for linear programming on a network of 400 transputers", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "Shell Research Center (KSLA)", address = "Amsterdam, The Netherlands", } @TechReport{int:Dowling1, author = "M. L. Dowling", title = "Comparing the affine and projective vector fields associated with linear programming", type = "{Technical Report}", year = "1989", institution = "Dept.\ of Management, University of Georgia", address = "Athens, GA~30602, USA", note = "Submitted to {\em Mathematical Programming}", } @Article{int:Du1, author = "D. Z. Du and F. Wu and X. S. Zhang", title = "Why is the objective function nonlinearized in the interior point methods for nonlinear programming?", journal = "Mathematics in Practice and Theory", volume = "2", year = "1990", pages = "63--68", note = "(In Chinese)", } @Article{int:Duff1, author = "I. S. Duff", title = "The solution of large--scale least--squares problems on supercomputers", journal = "Annals of Operations Research", volume = "22", year = "1990", pages = "241--252", } @Article{int:Economist1, key = "Economist", title = "Not so simplex", journal = "The Economist", year = "1984", month = "December 1,", } @TechReport{int:Edirisinghe1, author = "C. Edirisinghe and W. Ziemba", title = "A boundary point algorithm for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Commerce and Business Administration, University of British Columbia", address = "Vancouver, BC~V6T~1Y8, Canada", } @TechReport{int:ElBakry1, author = "A. S. El-Bakry and R. A. Tapia and Y. Zhang", title = "A study of indicators for identifying zero variables in interior--point methods", type = "{Technical Report}", number = "TR--91--15", year = "1991", institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @Article{int:Emmett1, author = "A. Emmett", title = "Karmarkar's algorithm~: {A} threat to simplex~?", journal = "IEEE Spectrum", year = "1985", month = dec, pages = "54--55", } @Article{int:Encheva1, author = "T. J. Encheva", title = "Computational comparisons for the method of centers of gravity of vertices", journal = "Serdica (Bulgaricae Mathematicae Publicationes)", volume = "16", number = "3", year = "1990", pages = "188--193", } @TechReport{int:Eriksson1, author = "J. R. Eriksson", title = "Algorithms for entropy and mathematical programming", type = "Link{\"o}ping Studies in Science and Technology Dissertations", number = "63", year = "1981", institution = "Dept.\ of Mathematics, Link{\"o}ping University", address = "S-58183~Link{\"o}ping, Sweden", } @TechReport{int:Eriksson2, author = "J. R. Eriksson", title = "An iterative primal--dual algorithm for linear programming", type = "{Technical Report}", number = "LiTH--MAT--R--1985--10", year = "1985", institution = "Dept.\ of Mathematics, Link{\"o}ping University", address = "S-58183~Link{\"o}ping, Sweden", } @TechReport{int:Eriksson3, author = "J. R. Eriksson", title = "Using the entropy function to get an interior point method for linear programming", type = "{Technical Report}", number = "LiTH--MAT--R--1990--02", year = "1990", institution = "Dept.\ of Mathematics, Link{\"o}ping University", address = "S-58183~Link{\"o}ping, Sweden", } @TechReport{int:Fang1, author = "W. Fang and W. Shi--Quan", title = "New algorithms for linear programming", type = "{Technical Report}", year = "19..(?)", institution = "Institute of Applied Mathematics, Academia Sinica", address = "Beijing, People Republic of China", } @TechReport{int:Fang2, author = "S. C. Fang and S. C. Puthenpura and R. Saigal and P. Sinha", title = "Stochastic linear programming via affine scaling and {Kalman}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Operations Research Program, North Carolina State University", address = "Raleigh, NC~27695, USA", } @TechReport{int:Fang3, author = "S. C. Fang", title = "A new unconstrained convex programming approach to linear programming", type = "{OR Research Report}", number = "243", year = "1990", institution = "Operations Research Program, North Carolina State University", address = "Raleigh, NC~27695, USA", note = "To appear in {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of Operations Research} 36(2), 1992", } @Article{int:Farrell1, author = "J. J. Farrell", title = "Recent advances in linear programming applied to global defense", journal = "Proceedings of the 27th IEEE Conference on Decision and Control, Austin, TX, USA", year = "1988", month = dec, pages = "242--243", } @TechReport{int:Fask1, author = "A. Fask and W. F. Walker", title = "A polynomial--time algorithm for solving transportation problems where the sources are bounded", type = "{Talk held at ORSA/TIMS Joint National Meeting in New Orleans, USA}", year = "1987", month = may, institution = "Farleigh Dickinson University", address = "Madison, NJ~07940, USA", } @Article{int:Ferris1, author = "M. C. Ferris and A. B. Philpott", title = "On the performance of {Karmarkar}'s algorithm", journal = "Journal of the Operational Research Society", volume = "39", year = "1988", pages = "257--270", } @Article{int:Ferris2, author = "M. C. Ferris and A. B. Philpott", title = "An interior point algorithm for semi--infinite linear programming", journal = "Mathematical Programming", volume = "43", year = "1989", pages = "257--276", } @InCollection{int:Fiacco1, author = "A. V. Fiacco", title = "Barrier methods in nonlinear programming", booktitle = "Operations Research Support Methodology", year = "1979", pages = "377--440", editor = "A. Holzman", publisher = "Marcel Dekker", address = "New York, NY, USA", } @Article{int:Fiacco2, author = "A. V. Fiacco", title = "Perturbed variations of penalty function methods --- example~: {Projective SUMT}", journal = "Annals of Operations Research", volume = "27", year = "1990", pages = "371--380", } @Book{int:Fiacco3, author = "A. V. Fiacco and G. P. McCormick", title = "Nonlinear Programming~: Sequential Unconstrained Minimization Techniques", publisher = "John Wiley \& Sons", year = "1968", address = "New York, NY, USA", note = "Reprint : Volume 4 of {\em SIAM Classics in Applied Mathematics}, SIAM Publications, Philadelphia, PA~19104--2688, USA, 1990", } @InCollection{int:Fletcher1, author = "R. Fletcher", title = "Recent developments in linear and quadratic programming", booktitle = "The State--of--the--Art in Numerical Analysis", publisher = "Oxford University Press", address = "Oxford, UK", editor = "A. Iserles and M. J. D. Powell", year = "1987", pages = "213--243, esp.~219--224", } @InBook{int:Fletcher2, author = "R. Fletcher", title = "Practical Methods of Optimization", chapter = "8.7~: {Polynomial} time algorithms", pages = "183--188", publisher = "John Wiley~\&~Sons", address = "New York, NY, USA", edition = "second", year = "1987", } @Article{int:Forrest1, author = "J. J. H. Forrest and J. A. Tomlin", title = "Vector processing in simplex and interior methods for linear programming", journal = "Annals of Operations Research", volume = "22", year = "1990", pages = "71--100", } @TechReport{int:Forsgren1, author = "A. L. Forsgren and W. Murray", title = "Newton methods for large--scale linear equality--constrained minimization", type = "{Technical Report}", number = "SOL~90--6", year = "1990", institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Fourer1, author = "R. Fourer and S. Mehrotra", title = "Performance of an augmented system approach for solving least--squares problems in an interior--point method for linear programming", type = "{Technical Report (in preparation)}", year = "1991", institution = "Dept.\ of Industrial Engineering and Management Sciences, Northwestern University", address = "Evanston, IL~60208, USA", } @Article{int:Fourer2, author = "R. Fourer and S. Mehrotra", title = "Performance of an augmented system approach for solving least--squares problems in an interior--point method for linear programming", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "26--31", } @Article{int:Fraley1, author = "C. Fraley", title = "Linear updates for a single -- phase projective method", journal = "Operations Research Letters", volume = "9", year = "1990", pages = "169--174", } @TechReport{int:Fraley2, author = "C. Fraley and J. P. Vial", title = "Single -- phase versus multiple -- phase projective methods for linear programming", type = "{Technical Report}", year = "1989", institution = "COMIN, University of Geneva", address = "2~Rue de Candolle, CH-1211~Geneva~4, Switzerland", } @InCollection{int:Fraley3, author = "C. Fraley and J. P. Vial", title = "Numerical study of projective methods for linear programming", booktitle = "Optimization~: Proceedings of the 5th French--German Conference in Castel--Novel, Varetz, France, October 1988", editor = "S. Dolecki", year = "1989", pages = "25--38", series = "Lecture Notes in Mathematics", volume = "1405", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:52:48 1995", } @Article{int:Franklin1, author = "J. Franklin", title = "Convergence in {Karmarkar}'s algorithm for linear programming", journal = "SIAM Journal on Numerical Analysis", volume = "24", year = "1987", pages = "928--945", } @TechReport{int:Freedman1, author = "B. A. Freedman and S. C. Puthenpura and L. P. Sinha", title = "A new affine scaling based algorithm for optimizing convex, nonlinear functions with linear constraints", type = "{Technical Report}", year = "1990", institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @Article{int:Freund1, author = "R. M. Freund", title = "An analogous of {Karmarkar}'s algorithm for inequality constrained linear programs, with a `new' class of projective transformations for centering a polytope", journal = "Operations Research Letters", volume = "7", year = "1988", pages = "9--13", } @Article{int:Freund2, author = "R. M. Freund", title = "Polynomial--time algorithms for linear programming based only on primal scaling and projected gradients of a potential function", journal = "Mathematical Programming", volume = "51", year = "1991", pages = "203--222", } @TechReport{int:Freund3, author = "R. M. Freund", title = "A generalization/extension of {Karmarkar}'s algorithm for inequality constrained linear programs based on projective centering of the polyhedra", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund4, author = "R. M. Freund", title = "Projective transformations for finding the w--center of a polyhedra", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund5, author = "R. M. Freund", title = "Projective transformations for interior point methods, {Part~I~: B}asic theory and linear programming", type = "{Working Paper}", number = "2049--88", year = "1988", month = oct, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund6, author = "R. M. Freund", title = "Projective transformations for interior point methods, {Part~II~: A}nalysis of an algorithm for finding the weighted center of a polyhedral system", type = "{Working Paper}", number = "2050--88", year = "1988", month = oct, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @Article{int:Freund7, author = "R. M. Freund", title = "Theoretical efficiency of a shifted barrier function algorithm for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "19--41", } @TechReport{int:Freund8, author = "R. M. Freund", title = "A potential--function reduction algorithm for solving a linear program directly from an infeasible `warm start'", type = "{Working Paper}", number = "3079--89--MS", year = "1989", institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @TechReport{int:Freund9, author = "R. M. Freund", title = "Theoretical efficiency of solving a linear program from an infeasible `warm start'", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund10, author = "R. M. Freund", title = "Interior point algorithms for solving a linear program directly from an infeasible `warm start'", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund11, author = "R. M. Freund", title = "Recent results and perspectives on solving linear programming from an infeasible `warm start'", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund12, author = "R. M. Freund", title = "Newton's method for general parametric center problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund13, author = "R. M. Freund and K. C. Tan", title = "A method for the parametric center problem, with a strictly monotone polynomial--time algorithm for linear programming", type = "{Working Paper}", number = "2100--89", year = "1989", institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", note = "Revised April 1990", } @TechReport{int:Freund14, author = "R. M. Freund and K. C. Tan", title = "A parametric center algorithm and a strictly monotonic central path algorithm for {LP}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund15, author = "R. M. Freund and K. C. Tan", title = "Newton's method for parametric center problems", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund16, author = "R. M. Freund", title = "Interior--point methods for linear programming~: {A} status report", type = "{Tutorial held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Freund17, author = "R. M. Freund", title = "Projective transformations for interior point algorithms, a superlinearly convergent algorithm for the w--center problem", type = "{Working Paper}", year = "1989", institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", note = "To appear in {\em Mathematical Programming}", } @TechReport{int:Freund18, author = "R. M. Freund", title = "A combined {phase~I -- phase~II} algorithm for {LP} based on the intuitive geometry of linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Sloan School of Management, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @Article{int:Fricker1, author = "F. Fricker", title = "{Komplexe Optimierungsaufgaben schneller l{\"o}sen~(Solving complex optimization problems faster)}", journal = "Frankfurter Allgemeine Zeitung, Sektion~: Natur und Wissen", year = "1985", month = "March 27,", note = "(In German)", } @TechReport{int:Frisch1, author = "K. R. Frisch", title = "The logarithmic potential method for convex programming", type = "Unpublished manuscript", year = "1955", month = may, institution = "Institute of Economics, University of Oslo", address = "Oslo, Norway", } @Article{int:Frisch2, author = "K. R. Frisch", title = "The multiplex method for linear programming", journal = "Sankhya", volume = "18", year = "1957", pages = "329--362", } @TechReport{int:Frisch3, author = "K. R. Frisch", title = "Principles of linear programming---{With} a particular reference to the double gradient form of the logarithmic potential method", type = "Memorandum", year = "1954", month = oct, institution = "Institute of Economics, University of Oslo", address = "Oslo, Norway", } @TechReport{int:Frisch4, author = "K. R. Frisch", title = "Linear dependencies and a mechanized form of the multiplex method for linear programming", type = "Memorandum", year = "1957", institution = "Institute of Economics, University of Oslo", address = "Oslo, Norway", } @Article{int:Fukushima1, author = "M. Fukushima and N. Arai and T. Ibaraki", title = "An interior method for nonlinear minimum cost network flow problems", journal = "Systems and Control (Japan)", volume = "31", number = "11", year = "1987", pages = "837--843", } @Article{int:Garcia1, author = "C. B. Garcia and F. J. Gould", title = "An application of homotopy to solving linear programs", journal = "Mathematical Programming", volume = "27", year = "1983", pages = "263--382", } @Article{int:Garey1, author = "M. R. Garey and D. M. Gay", title = "Letter from the {AT~\&~T Laboratories}", journal = "Mathematical Programming Society Committee on Algorithms (COAL) Newsletter", year = "1985", month = dec, } @InBook{int:Garfunkel1, author = "S. A. Garfunkel and L. A. Steen and J. Malkevitch", title = "For All Practical Purposes~: Introduction to Contemporary Mathematics", chapter = "4~: {Linear} programming~: {An} alternative to the simplex method", pages = "80--83, 362", publisher = "W. H. Freeman and Company", address = "New York, NY, USA", year = "1988", } @TechReport{int:Gay1, author = "D. M. Gay", title = "Sparse projections in {Karmarkar}'s linear programming algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA, USA}", year = "1985", month = nov, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Gay2, author = "D. M. Gay", title = "Pictures of {Karmarkar}'s linear programming algorithm", type = "{Computer Science Technical Report}", number = "136", year = "1987", institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Gay3, author = "D. M. Gay", title = "A variant of {Karmarkar}'s linear programming algorithm for problems in standard form", journal = "Mathematical Programming", volume = "37", year = "1987", pages = "81--90", note = "Errata in {\em Mathematical Programming}, 40:111, 1988", } @Article{int:Gay4, author = "D. M. Gay", title = "Massive memory buys little speed for complete, in--core sparse {Cholesky} factorizations on some scalar computers", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "291--314", } @InCollection{int:Gay5, author = "D. M. Gay", title = "Stopping tests that compute optimal solutions for interior--point linear programming algorithms", booktitle = "Advances in Numerical Partial Differential Equations and Optimization", year = "1991", pages = "17--42", publisher = "SIAM Publications", address = "Philadelphia, PA, USA", } @Article{int:Gay6, author = "D. M. Gay and N. K. Karmarkar and K. G. Ramakrishnan", title = "The {Karmarkar} algorithm~: {Adding} wings to linear programming", journal = "Record AT~\&~T~Bell Laboratories", volume = "64", number = "2", year = "1986", pages = "4--10", } @Book{int:Gay7, author = "D. M. Gay and M. Kojima and R. A. Tapia", title = "Interior Point Methods for Linear Programming", year = "1991", month = jul, series = "Linear Algebra and Its Applications", volume = "152", publisher = "North Holland", address = "Amsterdam, The Netherlands", } @InBook{int:Gelbaum1, author = "B. R. Gelbaum", title = "Linear Algebra~: Basics, Practice and Theory", chapter = "5.7~: {The K}armarkar algorithm", pages = "504--527", publisher = "North Holland", address = "New York, NY, USA", year = "1989", } @TechReport{int:Ghare1, author = "P. Ghare", title = "Free decision variables and simplified interior point methods for linear programming", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "Northern Virginia Graduate Centre", address = "USA", } @Article{int:Ghellinck1, author = "{G. de} Ghellinck and J. P. Vial", title = "A polynomial {Newton} method for linear programming", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "425--453", } @Article{int:Ghellinck2, author = "{G. de} Ghellinck and J. P. Vial", title = "An extension of {Karmarkar}'s algorithm for solving a system of linear homogeneous equations on the simplex", journal = "Mathematical Programming", volume = "39", year = "1987", pages = "79--92", } @TechReport{int:Ghellinck3, author = "{G. de} Ghellinck and J. P. Vial", title = "A unified approach to projective and affine algorithms for linear programming", type = "{Talk held at the EURO/TIMS Joint International Conference on Operational Research in Paris, France}", year = "1988", month = jul, institution = "Center of Operations Research and Econometrics, Universite Catholique de Louvain", address = "B-1348~Louvain-la-Neuve, Belgium", } @TechReport{int:Gill1, author = "P. E. Gill and W. Murray and M. A. Saunders", title = "A single -- phase dual barrier method for linear programming", type = "{Technical Report}", number = "SOL~88--10", year = "1988", month = aug, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Gill2, author = "P. E. Gill and W. Murray and M. A. Saunders", title = "Interior--point methods for linear programs : {A} challenge to the simplex method", type = "{Technical Report}", number = "SOL~88--14", year = "1988", month = jul, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Gill3, author = "P. E. Gill and W. Murray and M. A. Saunders and M. H. Wright", title = "A note on nonlinear approaches to linear programming", type = "{Technical Report}", number = "SOL~86--7", year = "1986", month = apr, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Gill4, author = "P. E. Gill and W. Murray and M. A. Saunders and M. H. Wright", title = "Convergence results for a shifted barrier linear programming method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Gill5, author = "P. E. Gill and W. Murray and M. A. Saunders and M. H. Wright", title = "Shifted barrier methods for linear programming", type = "{Technical Report}", number = "SOL~88--9", year = "1988", month = aug, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Gill6, author = "P. E. Gill and A. Marxen and W. Murray and M. A. Saunders and M. H. Wright", title = "Solution of the primal {LP}-problem by a barrier method~: {Some} implementation aspects", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Gill7, author = "P. E. Gill and W. Murray and M. A. Saunders and J. A. Tomlin and M. H. Wright", title = "On projected {Newton} barrier methods for linear programming and an equivalence to {Karmarkar}'s projective method", journal = "Mathematical Programming", volume = "36", year = "1986", pages = "183--209", } @TechReport{int:Gill8, author = "P. E. Gill and W. Murray and D. B. Ponceleon and M. A. Saunders", title = "Primal--dual methods for linear programming", type = "{Technical Report}", number = "SOL~91-3", year = "1991", month = may, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Gill9, author = "P. E. Gill and W. Murray and D. B. Ponceleon and M. A. Saunders", title = "Solving reduced {KKT}--systems in barrier methods for linear and quadratic programming", type = "{Technical Report}", number = "SOL~91-7", year = "1991", month = jul, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Book{int:Gill10, author = "P. E. Gill and W. Murray and M. H. Wright", title = "Numerical Linear Algebra and Optimization, {Vol}.\ 2", publisher = "Addison Wesley Publishing Company", year = "1991/92", address = "Amsterdam, The Netherlands", note = "Chapter on interior point methods", } @TechReport{int:Gill11, author = "P. E. Gill and W. Murray and D. B. Ponceleon and M. A. Saunders", title = "Preconditioners for indefinite systems arising in optimization", type = "{Technical Report}", number = "SOL~90-8", year = "1990", month = jun, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Glassman1, author = "N. D. Glassman", title = "{ONR (Office of Naval Research)} focuses on interior methods", journal = "SIAM News", volume = "20", number = "2", pages = "12", year = "1987", month = mar, } @Article{int:Gleick1, author = "J. Gleick", title = "Breakthrough in problem solving", journal = "The New York Times", year = "1984", month = "November 19, ", } @TechReport{int:Goessl1, author = "H. Goessl", title = "{Eine Modifikation des Verfahrens von Karmarkar basierend auf einer Formulierung des Algorithmus im Originalproblem~(A modification of Karmarkar's algorithm based on a formulation of the algorithm in the original problem)}", type = "{Interner Bericht der intergrierten Arbeitsgruppe Mathematische Probleme aus dem Ingenieurbereich}", year = "1986", month = oct, institution = "Fachbereich Mathematik, Gesamthochschule Wuppertal", address = "D-5600~Wuppertal~1, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:53:03 1995", } @TechReport{int:Goessl2, author = "H. Goessl", title = "{Eine Verallgemeinerung und eine duale Variante des Verfahrens von de Ghellinck und Vial zur linearen Optimierung~(A generalization and a dual variant of the algorithm of de Ghellinck and Vial for linear programming)}", type = "{Interner Bericht der intergrierten Arbeitsgruppe Mathematische Probleme aus dem Ingenieurbereich}", year = "1987", month = dec, institution = "Fachbereich Mathematik, Gesamthochschule Wuppertal", address = "D-5600~Wuppertal~1, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:53:16 1995", } @PhdThesis{int:Goessl3, author = "H. Goessl", title = "{Varianten der polynomialen Newtonmethode zur linearen Optimierung~(Variants of the polynomial Newton method for linear programming)}", year = "1989", school = "Fachbereich Mathematik, Gesamthochschule Wuppertal", address = "D-5600~Wuppertal~1, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:53:18 1995", } @InCollection{int:Goffin1, author = "J. L. Goffin", title = "Affine and projective methods in nondifferentiable optimization", booktitle = "Trends in Mathematical Optimization~: Proceedings of the 4th French--German Conference on Optimization in Irsee, West Germany, April 1986", editor = "K. H. Hoffmann and J. B. Hiriat--Urruty and C. Lemarechal and J. Zowe", series = "International Series of Numerical Mathematics", volume = "84", year = "1988", pages = "79--91", publisher = "Birkh{\"a}user Verlag", address = "Basel, Switzerland", bibdate = "Sat Dec 30 09:53:28 1995", } @TechReport{int:Goffin2, author = "J. L. Goffin", title = "Decomposition and large scale optimization with the interior point algorithms", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Faculty of Management, McGill University", address = "Montreal, Ontario, Canada", } @Article{int:Goffin3, author = "J. L. Goffin and J. P. Vial", title = "Cutting planes and column generation techniques with the projective algorithm", journal = "Journal of Optimization Theory and Applications", volume = "65", year = "1990", pages = "409--429", } @TechReport{int:Goffin4, author = "J. L. Goffin and A. Haurie and J. P. Vial", title = "Decomposition and nondifferentiable optimization with the projective algorithm", type = "Preprint", number = "G--89--25", year = "1989", institution = "Faculty of Management, McGill University", address = "Montreal, Ontario, Canada", } @TechReport{int:Goffin5, author = "J. L. Goffin and J. P. Vial", title = "Short steps with {Karmarkar}'s projective algorithm for linear programming", type = "Manuscript", year = "1990", institution = "Department d'Economic Commerciale et Industrielle, Universite de Geneve", address = "Geneve, Switzerland", } @TechReport{int:Goffin6, author = "J. L. Goffin and J. P. Vial", title = "On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm", type = "{Working Paper}", year = "1989", institution = "Faculty of Management, McGill University", address = "Montreal, Ontario, Canada", } @TechReport{int:Goffin7, author = "J. L. Goffin and A. Haurie and J. P. Vial and D. L. Zhu", title = "Using central prices in the decomposition of linear programs", type = "{Research Working Paper Series}", year = "1991", institution = "Faculty of Management, McGill University", address = "Montreal, Ontario, Canada", } @TechReport{int:Goffin8, author = "J. L. Goffin", title = "Affine methods in nondifferentiable optimization", type = "{CORE Discussion Paper}", number = "8744", year = "1987", institution = "Center for Operations Research and Econometrics, Universite Catholique de Louvain", address = "B-1348 Louvain-la-Neuve, Belgium", } @InCollection{int:Goldberg1, author = "A. V. Goldberg and S. A. Plotkin and D. B. Shmoys and E. Tardos", title = "Interior--point methods in parallel computation", booktitle = "Proceedings of the 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 1989", year = "1990", pages = "350--355", publisher = "IEEE Computer Society Press", address = "Los Alamitos, CA, USA", } @TechReport{int:Goldfarb1, author = "D. Goldfarb", title = "A relaxed version of {Karmarkar}'s method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach, FL, USA}", year = "1986", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Goldfarb2, author = "D. Goldfarb", title = "A primal projective interior point method for linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @Article{int:Goldfarb3, author = "D. Goldfarb and S. Liu", title = "An ${O(n^{3}L)}$ primal interior point algorithm for convex quadratic programming", journal = "Mathematical Programming", volume = "49", year = "1990/91", pages = "325--340", } @Article{int:Goldfarb4, author = "D. Goldfarb and S. Mehrotra", title = "A relaxed version of {Karmarkar}'s method", journal = "Mathematical Programming", volume = "40", year = "1988", pages = "289--315", } @Article{int:Goldfarb5, author = "D. Goldfarb and S. Mehrotra", title = "Relaxed variants of {Karmarkar}'s algorithm for linear programs with unknown optimal objective value", journal = "Mathematical Programming", volume = "40", year = "1988", pages = "183--195", } @TechReport{int:Goldfarb6, author = "D. Goldfarb and S. Mehrotra", title = "A homogeneous equations variant of {Karmarkar}'s algorithm for solving linear programs", type = "{Talk held at ORSA/TIMS Joint National Meeting in New Orleans, USA}", year = "1987", month = may, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @Article{int:Goldfarb7, author = "D. Goldfarb and S. Mehrotra", title = "A self--correcting version of {Karmarkar}'s algorithm", journal = "SIAM Journal on Numerical Analysis", volume = "26", year = "1989", pages = "1006--1015", } @InCollection{int:Goldfarb8, author = "D. Goldfarb and M. J. Todd", title = "Karmarkar's projective scaling algorithm", booktitle = "Optimization", publisher = "North Holland", address = "Amsterdam, The Netherlands", editor = "G. L. Nemhauser and A. H. G. {Rinnoy Kan} and M. J. Todd", series = "Handbooks in Operations Research and Management Science", volume = "1", year = "1989", pages = "141--170", } @Article{int:Goldfarb9, author = "D. Goldfarb and S. Liu and S. Wang", title = "A logarithmic barrier function algorithm for quadratically constrained convex programming", journal = "SIAM Journal on Optimization", volume = "1", year = "1991", pages = "252--267", } @TechReport{int:Goldfarb10, author = "D. Goldfarb and S. Liu", title = "Interior point potential function reduction algorithm for solving convex quadratic programming", type = "{Technical Report}", year = "1990", institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @Article{int:Goldfarb11, author = "D. Goldfarb and D. Xiao", title = "A primal projective interior point method for linear programming", journal = "Mathematical Programming", volume = "51", year = "1991", pages = "17--43", } @Article{int:Golshtejn1, author = "E. G. Gol'shtejn and A. S. Nemirovsky and Y. E. Nesterov", title = "On some recent advances in optimization", journal = "Ekonomika i Matematickeskie Metody (Moscow)", volume = "26", number = "1", year = "1990", pages = "178--190", note = "(In Russian)", } @TechReport{int:Gondzio1, author = "J. Gondzio", title = "Splitting dense columns of constraint matrix in interior point methods for large scale linear programming", type = "Cahier", number = "105", year = "1991", month = jul, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", note = "Former title~: {\em On handling dense columns of constraint matrix in interior point methods of large scale linear programming}, April 1991. To appear in {\em Optimization}", } @TechReport{int:Gondzio2, author = "J. Gondzio", title = "An advanced implementation of {Cholesky} factorization for computing projections in interior point methods for large scale linear programming", type = "Cahier", number = "107", year = "1991", month = dec, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @TechReport{int:Gondzio3, author = "J. Gondzio and D. Tachat", title = "The design and application of the {IMPLO -- A FORTRAN} library for linear optimization with interior point methods", type = "Cahier", number = "108", year = "1992", month = jan, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @TechReport{int:Gonzaga1, author = "C. C. Gonzaga", title = "New results in conical projection methods for mathematical programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach, FL, USA}", year = "1986", month = oct, institution = "Dept.\ of Electrical Engineering and Computer Science, University of California", address = "Berkeley, CA~94720, USA", } @Article{int:Gonzaga2, author = "C. C. Gonzaga", title = "Search directions for interior linear programming methods", journal = "Algorithmica", volume = "6", year = "1991", pages = "153--181", } @Article{int:Gonzaga3, author = "C. C. Gonzaga", title = "Interior point algorithms for linear programming problems with inequality constraints", journal = "Mathematical Programming", volume = "52", year = "1991", pages = "209--225", } @Article{int:Gonzaga4, author = "C. C. Gonzaga", title = "Polynomial affine algorithms for linear programming", journal = "Mathematical Programming", volume = "49", year = "1990", pages = "7--21", } @Article{int:Gonzaga5, author = "C. C. Gonzaga", title = "Conical projection algorithms for linear programming", journal = "Mathematical Programming", volume = "43", year = "1989", pages = "151--173", } @InCollection{int:Gonzaga6, author = "C. C. Gonzaga", title = "An algorithm for solving linear programming problems in ${O(n^{3}L)}$ operations", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", editor = "N. Megiddo", year = "1989", pages = "1--28", } @Article{int:Gonzaga7, author = "C. C. Gonzaga", title = "Large steps path--following methods for linear programming, {Part~I}~: {Barrier} function method", journal = "SIAM Journal on Optimization", volume = "1", year = "1991", pages = "268--279", } @Article{int:Gonzaga8, author = "C. C. Gonzaga", title = "Large steps path--following methods for linear programming, {Part~II}~: {Potential} reduction method", journal = "SIAM Journal on Optimization", volume = "1", year = "1991", pages = "280--292", } @TechReport{int:Gonzaga9, author = "C. C. Gonzaga", title = "An overview of ${O(\sqrt{n}L)}$--iteration algorithms for linear programming", type = "{Talk held at the 14th Conference on the Mathematics of Operations Research in Dalfsen, The Netherlands}", year = "1990", month = jan, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gonzaga10, author = "C. C. Gonzaga", title = "A larger step path--following potential reduction algorithm for linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gonzaga11, author = "C. C. Gonzaga", title = "Large steps potential reduction algorithms for linear programming", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gonzaga12, author = "C. C. Gonzaga and M. J. Todd", title = "An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine algorithm for linear programming", type = "{Technical Report}", number = "862", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Gonzaga13, author = "C. C. Gonzaga", title = "A conical projection algorithm for linear programming", type = "Memorandum", number = "UCB/ERL~M85/61", year = "1985", month = jul, institution = "Electronics Research Laboratory, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Gonzaga14, author = "C. C. Gonzaga", title = "On lower bound updates in primal potential reduction methods for linear programming", type = "{Technical Report}", number = "ES--227/90", year = "1990", institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @TechReport{int:Gonzaga15, author = "C. C. Gonzaga", title = "A simple representation of {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1988", month = may, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gonzaga16, author = "C. C. Gonzaga", title = "On the convergence of the large step affine--scaling algorithm for linear programming", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gonzaga17, author = "C. C. Gonzaga", title = "Trust region minimization in conical projection algorithms", type = "{Talk held at the Eleventh IFORS International Conference on Operations Research in Buenos Aires, Argentina}", year = "1987", month = aug, institution = "Dept.\ of Electrical Engineering and Computer Science, University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Gonzaga18, author = "C. C. Gonzaga", title = "Convergence of the large step primal affine--scaling algorithm for primal nondegenerate linear programs", type = "{Technical Report}", number = "ES--230/90", year = "1990", month = sep, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gonzaga19, author = "C. C. Gonzaga", title = "Path following methods for linear programming", type = "{Technical Report}", number = "ES--246/91", year = "1991", month = nov, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", note = "To appear in {\em SIAM Reviews 34, 1991}", } @TechReport{int:Gonzaga20, author = "C. C. Gonzaga", title = "Path--following algorithms for linear and quadratic programming", type = "{Talk held at the Third SIAM Conference on Optimization in Boston, MA, USA}", year = "1989", month = apr, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @Article{int:Gonzaga21, author = "C. C. Gonzaga", title = "An interior trust region method for linearly constrained optimization", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "55--66", } @TechReport{int:Gonzaga22, author = "C. C. Gonzaga and L. A. Carlos", title = "A primal affine--scaling algorithm for linearly constrained convex programs", type = "{Technical Report}", number = "ES--238/90", year = "1990", month = dec, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Gray1, author = "P. Gray and J. A. Kaliski and Y. Ye", title = "An implementation of the build--up interior method for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "College of Business, Dept.\ of Management Sciences, University of Iowa", address = "Iowa City, IA~52242, USA", } @Article{int:Groetschel1, author = "M. Gr{\"o}tschel", title = "{Patente f{\"u}r mathematische Algorithmen. (Patents for mathematical algorithms)}", journal = "Mitteilungen der Deutschen Mathematiker--Vereinigung", volume = "{Heft 2}", year = "1991", month = apr, pages = "52--56", note = "(In German)", } @TechReport{int:Grover1, author = "L. K. Grover", title = "Strongly polynomial interior point algorithm for a class of linear programming problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "School of Electrical Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Grover2, author = "L. K. Grover", title = "Interior point methods for unimodular linear programming", type = "{Technical Report}", year = "1990", institution = "School of Electrical Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Grover3, author = "L. K. Grover", title = "A force based approach to interior point algorithms for linear programming", type = "{Technical Report}", year = "1990", institution = "School of Electrical Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Gueler1, author = "O. G{\"u}ler and Y. Ye", title = "Interior point algorithms for {LP} generate strictly complementary solutions", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Gueler2, author = "O. G{\"u}ler", title = "Existence of interior points and interior paths in nonlinear monotone complementarity problems", type = "{Working Paper}", year = "1990", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Gueler3, author = "O. G{\"u}ler and Y. Ye", title = "Convergence behavior of some interior point algorithms", type = "{Working Paper}", number = "91--04", year = "1991", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", note = "To appear in {\em Mathematical Programming}", } @TechReport{int:Gueler4, author = "O. G{\"u}ler", title = "Path following and potential reduction algorithms for nonlinear monotone complementarity problems", type = "{Working Paper (in preparation)}", year = "1991", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Gueler5, author = "O. G{\"u}ler", title = "An interior point algorithm for nonlinear monotone complementarity problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Gueler6, author = "O. G{\"u}ler and {D. den} Hertog and C. Roos and T. Terlaky and T. Tsuchiya", title = "Degeneracy in interior point methods for linear programming", type = "{Technical Report}", year = "1991", month = dec, institution = "Faculty of Technical Mathematics and Computer Science, TU Delft", address = "NL-2600~GA~Delft, The Netherlands", } @InBook{int:Haemmerlin1, author = "G. H{\"a}mmerlin and K. H. Hoffmann", title = "Numerische Mathematik", chapter = "9.4.4~: {Polynomiale Algorithmen}", year = "1991", pages = "424--430", publisher = "Springer-Verlag", address = "Berlin, Germany", edition = "second", note = "(In German)", bibdate = "Sat Dec 30 09:53:34 1995", } @Article{int:Hamala1, author = "M. Hamala", title = "A general approach to interior point transformation methods for mathematical programming", journal = "Acta Mathematica Universitatis Comenianae (Comenius University Czechoslovakia)", volume = "54/55", year = "1989", pages = "243--266", } @Article{int:Hamilton1, author = "B. C. Hamilton and D. E. Stein", title = "{AT~\&~T's KORBX System~: Solving} the unsolvable", journal = "AT~\&~T Technology", volume = "4", number = "3", year = "1989", pages = "36--41", } @TechReport{int:Han1, author = "C. G. Han and P. M. Pardalos and Y. Ye", title = "Interior point approaches to nonconvex programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Computer Science Department, The Pennsylvania State University", address = "University Park, PA~16802, USA", } @InCollection{int:Han2, author = "C. G. Han and P. M. Pardalos and Y. Ye", title = "Computational aspect of an interior point algorithm for quadratic programming problems with box constraints", booktitle = "Large--Scale Numerical Optimization, Papers from the Workshop held at Cornell University, Ithaca, NY, USA, October 1989", series = "SIAM Proceedings in Applied Mathematics", volume = "46", year = "1990", pages = "92--112", editor = "T. F. Coleman and Y. Li", publisher = "Society of Industrial and Applied Mathematics (SIAM)", address = "Philadelphia, PA, USA", } @TechReport{int:Han3, author = "C. G. Han and P. M. Pardalos and Y. Ye", title = "On potential reduction algorithms for some entropy optimization problems", type = "{Technical Report}", number = "CS--91--02", year = "1991", institution = "Computer Science Department, The Pennsylvania State University", address = "University Park, PA~16802, USA", } @TechReport{int:Han4, author = "C. G. Han and P. M. Pardalos and Y. Ye", title = "Solving some engineering problems using an interior--point algorithm", type = "{Technical Report}", number = "CS--91--04", year = "1991", institution = "Computer Science Department, The Pennsylvania State University", address = "University Park, PA~16802, USA", } @Article{int:Harker1, author = "P. T. Harker and B. Xiao", title = "A polynomial--time algorithm for affine variational inequalities", journal = "Applied Mathematics Letters", volume = "4", number = "2", year = "1991", pages = "31--34", } @TechReport{int:Haverly1, author = "C. A. Haverly", title = "Behavior of the simplex and {Karmarkar} algorithms", type = "{Talk held at the 12th Symposium on Mathematical Programming in Cambridge, MA, USA}", year = "1985", institution = "Haverly Systems Inc.", address = "Denville, NJ~07834, USA", } @TechReport{int:Haverly2, author = "C. A. Haverly", title = "Studies on behavior of the {Karmarkar} method", type = "{Technical Report}", year = "1985", institution = "Haverly Systems Inc.", address = "Denville, NJ~07834, USA", } @TechReport{int:Haverly3, author = "C. A. Haverly", title = "Results of a new series of case runs using {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1985", institution = "Haverly Systems Inc.", address = "Denville, NJ~07834, USA", } @TechReport{int:Heindl1, author = "G. Heindl", title = "{Eine Implementierung des Karmarkar Verfahrens~(An implementation of Karmarkar's algorithm)}", type = "{Interner Bericht der intergrierten Arbeitsgruppe Mathematische Probleme aus dem Ingenieurbereich}", year = "1985", month = feb, institution = "Fachbereich Mathematik, Gesamthochschule Wuppertal", address = "D-5600~Wuppertal~1, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:53:38 1995", } @TechReport{int:Herskovits1, author = "J. Herskovits and J. Asquier", title = "A quasi--{Newton} interior point algorithm for nonlinear constrained optimization", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Center of Technology, COPPE Federal University of Rio de Janeiro", address = "21941 Rio de Janeiro, Brazil", } @MastersThesis{int:Hertog1, author = "{D. den} Hertog", title = "Interior point methods for linear programming", year = "1989", month = may, school = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Hertog2, author = "{D. den} Hertog and C. Roos", title = "A survey of search directions in interior point methods for linear programming", type = "{Technical Report}", number = "89--65", year = "1989", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @TechReport{int:Hertog3, author = "{D. den} Hertog and C. Roos and T. Terlaky", title = "A potential reduction method for a class of smooth convex programming problems", type = "{Technical Report}", number = "90--01", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Hertog4, author = "{D. den} Hertog and C. Roos and T. Terlaky", title = "On the classical logarithmic barrier function method for a class of smooth convex programming problems", type = "{Technical Report}", number = "90--28", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Hertog5, author = "{D. den} Hertog and C. Roos and J. P. Vial", title = "An ${O(n^{0.5}L)}$ complexity reduction for long step path following methods", type = "Revised version of {Technical Report}", number = "89--85", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", note = "To appear in {\em SIAM Journal on Optimization}", } @Article{int:Hertog6, author = "{D. den} Hertog and C. Roos and T. Terlaky", title = "A potential reduction variant of {Renegar}'s short--step path--following method for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "43--68", } @TechReport{int:Hertog7, author = "{D. den} Hertog and C. Roos and T. Terlaky", title = "Inverse barrier methods for linear programming", type = "{Technical Report}", number = "91--27", year = "1991", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @Article{int:Hertog8, author = "{D. den} Hertog and C. Roos and T. Terlaky", title = "A polynomial method of weighted centers for convex quadratic programming", journal = "Journal of Information \& Optimization Sciences", volume = "12", number = "2", year = "1991", pages = "187--205", } @TechReport{int:Hertog9, author = "{D. den} Hertog and C. Roos and T. Terlaky", title = "A build--up variant of the path--following method for {LP}", type = "{Technical Report}", number = "91--47", year = "1991", month = jun, institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Hertog10, author = "{D. den} Hertog and C. Roos and J. P. Vial", title = "A complexity reduction for the long--step path--following for linear programming", type = "{Technical Report}", number = "90--28", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Hertog11, author = "{D. den} Hertog and C. Roos and J. P. Vial", title = "Polynomial--time long--steps algorithms for linear programming based on the use of the logarithmic barrier function", type = "{Manuscript}", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @Article{int:Herzel1, author = "S. Herzel and M. C. Recchioni and F. Zirilli", title = "A quadratically convergent method for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "255--289", } @Article{int:Hettich1, author = "R. Hettich and G. Margraff", title = "Some experiments with {Karmarkar}'s algorithm", journal = "Optimization", volume = "19", year = "1988", pages = "653--664", } @Article{int:Hettich2, author = "R. Hettich and M. Ries", title = "A modified scaling algorithm for {LP}", journal = "Optimization", volume = "21", year = "1990", pages = "709--721", } @InBook{int:Hillier1, author = "F. S. Hillier and G. J. Lieberman", title = "Introduction to Operations Research", chapter = "4.9~: {New} developments, pages 100--104, chapter~9.4~: {An} interior--point algorithm", year = "1990", pages = "312--323", publisher = "McGraw--Hill", address = "", edition = "fifth", } @TechReport{int:Ho1, author = "J. K. Ho", title = "Linear programming with spreadsheet macros", type = "{Technical Report}", year = "1987", institution = "Management Science Program, University of Tennessee", address = "615-SMC, Knoxville, TN~37996-0562, USA", } @Article{int:Hoffmann1, author = "A. J. Hoffmann and M. Mannos and D. Sokolowsky and N. Wiegmann", title = "Computational experience in solving linear programs", journal = "Journal of the Society for Industrial and Applied Mathematics (SIAM)", volume = "1", year = "1953", pages = "17--33", } @Article{int:Hooker1, author = "J. N. Hooker", title = "Karmarkar's linear programming algorithm", journal = "Interfaces", volume = "16", number = "4", year = "1986", pages = "75--90", note = "Errata in {\em Interfaces}, 17(1):128, 1987", } @TechReport{int:Houck1, author = "D. Houck", title = "Introduction to the {AT~\&~T~KORBX System}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Housos1, author = "E. C. Housos and C. C. Huang and J. M. Liu", title = "Parallel vector computational considerations on the {AT~\&~T~KORBX System}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "AT~\&~T~Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @Article{int:Housos2, author = "E. C. Housos and C. C. Huang and J. M. Liu", title = "Parallel algorithms for the {AT~\&~T~KORBX System}", journal = "AT~\&~T~Technical Journal", volume = "68", year = "1989", pages = "37--47", } @Misc{int:Hu1, author = "T. C. Hu", title = "Linear programming algorithms and computational results", year = "1987", address = "Dept.\ of Computer Science, University of California, La Jolla, CA 92093, USA", note = "Panel--Discussion at the ORSA/TIMS Joint National Meeting in St.~Louis, October 1987", } @TechReport{int:Huang1, author = "S. Huang", title = "A primal--dual algorithm for linear programming", type = "{Technical Report}", year = "1989", institution = "College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @TechReport{int:Huang2, author = "S. Huang and K. O. Kortanek", title = "A simultaneous primal-- and dual--potential reduction algorithm for linear programming", type = "{Working Paper Series}", number = "89--2", year = "1989", institution = "College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @TechReport{int:Huang3, author = "S. Huang and K. O. Kortanek", title = "A large--step simultaneous primal--dual potential reduction algorithm for {LP}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @InCollection{int:Huard1, author = "P. Huard", title = "Resolution of mathematical programming with nonlinear constraints by the method of centers", booktitle = "Nonlinear Programming", editor = "J. Abadie", year = "1967", pages = "207--219", publisher = "North Holland", address = "Amsterdam, The Netherlands", } @InCollection{int:Huard2, author = "P. Huard", title = "A method of centers by upper--bounding functions with applications", booktitle = "Nonlinear Programming~: Proceedings of a Symposium held at the University of Wisconsin, Madison, Wisconsin, USA, May 1970", editor = "J. B. Rosen and O. L. Mangasarian and K. Ritter", year = "1970", pages = "1--30", publisher = "Academic Press", address = "New York, USA", } @TechReport{int:Ikura1, author = "Y. Ikura and D. Stein", title = "Computational experience with a {Karmarkar}--based approach to solve multi--period, multi--refinery production models", type = "{Talk held at the 12th Triennial Conference on Operations Research in Athens, Greece}", year = "1990", month = jun, institution = "AT~\&~T~Bell Laboratories", } @Article{int:Imai1, author = "H. Imai", title = "Extensions of the multiplicative penalty function for linear programming", journal = "Journal of the Operations Research Society of Japan", volume = "30", year = "1987", pages = "160--180", } @Article{int:Imai2, author = "H. Imai", title = "On the convexity of the multiplicative version of {Karmarkar}'s potential function", journal = "Mathematical Programming", volume = "40", year = "1988", pages = "29--32", } @Article{int:Imai3, author = "H. Imai", title = "Recent trends in linear programming", journal = "Journal of the Institute of Electronics, Information and Communication Engineers (Japan)", volume = "72", number = "10", year = "1989", pages = "1053--1058", note = "(In Japanese)", } @Article{int:Imai4, author = "H. Imai", title = "On the polynomiality of the multiplicative penalty function method for linear programming and related inscribed ellipsoids", journal = "Transactions of the Institute of Electronics, Information and Communication Engineers (Japan)", volume = "E74", number = "4", year = "1991", month = apr, pages = "669--671", } @TechReport{int:Iri1, author = "M. Iri", title = "Another `simple and fast' algorithm for linear programming", type = "{Talk held at the 12th Symposium on Mathematical Programming in Cambridge, MA, USA}", year = "1985", institution = "Dept.\ of Mathematical Engineering and Instrumentation Physics, University of Tokyo", address = "Tokyo, Japan", } @TechReport{int:Iri2, author = "M. Iri", title = "Integrability of vector and polyvector fields associated with interior point methods", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Dept.\ of Mathematical Engineering and Instrumentation Physics, University of Tokyo", address = "Tokyo, Japan", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @Article{int:Iri3, author = "M. Iri and H. Imai", title = "A multiplicative penalty function for linear programming-- another `new and fast' algorithm", journal = "Proceedings of the 6th Mathematical Programming Symposium of Japan, Tokyo, Japan", year = "1985", pages = "97--120", } @Article{int:Iri4, author = "M. Iri and H. Imai", title = "A multiplicative barrier function method for linear programming", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "455--482", } @InCollection{int:Iri5, author = "M. Iri and H. Imai", title = "Theory of the multiplicative penalty function method for linear programming", booktitle = "Discrete Algorithms and Complexity~: Proceedings of the Japan--US Joint Seminar, Kyoto, Japan, June 1986", editor = "D. S. Johnson and T. Nishizeki and A. Nozaki and H. S. Wilf", year = "1987", pages = "417--435", publisher = "Academic Press", address = "New York, NY, USA", } @TechReport{int:Iri6, author = "M. Iri", title = "A proof of the polynomiality of the {Iri--Imai} method for linear programming", type = "{Technical Report}", year = "1991", institution = "Dept.\ of Mathematical Engineering and Instrumentation Physics, University of Tokyo", address = "Tokyo, Japan", } @TechReport{int:Jan1, author = "G. M. Jan and S. C. Fang", title = "A variant of affine--scaling method for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "North Carolina State University", address = "Raleigh, NC~27695-7913, USA", } @Article{int:Jan2, author = "G. M. Jan and S. C. Fang", title = "A new variant of the primal affine scaling method for linear programs", journal = "Optimization", volume = "22", number = "5", year = "1991", pages = "681--715", } @PhdThesis{int:Jan3, author = "G. M. Jan", title = "A new variant of the primal affine scaling algorithm for linear programs", year = "1990", month = jul, school = "Dept.\ of Operations Research, North Carolina State University", address = "Raleigh, NC~27695-7913, USA", } @Article{int:Janacek1, author = "J. Janacek", title = "{Perspektivy Karmarkarova algorithmu v linearnim programovani (Perspectives of Karmarkar's algorithm in linear programming)}", journal = "Ekonomicko--Matematicky Obzor (Czechoslovakia)", volume = "25", number = "1", year = "1989", pages = "50--63", note = "(In Czech)", } @Article{int:Jarre1, author = "F. Jarre", title = "On the convergence of the method of analytic centers when applied to convex quadratic programs", journal = "Mathematical Programming", volume = "49", year = "1990/91", pages = "341--358", } @TechReport{int:Jarre2, author = "F. Jarre", title = "The method of analytic centers for smooth convex programs", type = "Preprint", number = "165", year = "1989", institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:53:42 1995", } @InCollection{int:Jarre3, author = "F. Jarre", title = "On the method of analytic centers for solving smooth convex programs", booktitle = "Optimization~: Proceedings of the 5th French--German Conference in Castel--Novel, Varetz, France, October 1988", editor = "S. Dolecki", year = "1989", pages = "69--86", series = "Lecture Notes in Mathematics", volume = "1405", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:01 1995", } @TechReport{int:Jarre4, author = "F. Jarre", title = "A homotopy method for convex programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:54:03 1995", } @InCollection{int:Jarre5, author = "F. Jarre and G. Sonnevend and J. Stoer", title = "An implementation of the method of analytic centers", booktitle = "Analysis and Optimization of Systems", editor = "A. Bensoussan and J. L. Lions", year = "1988", pages = "297--308", series = "Lecture Notes in Control and Information Sciences", volume = "111", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:06 1995", } @TechReport{int:Jarre6, author = "F. Jarre", title = "Convergence of the method of analytic centers for generalized convex programs", type = "DFG--Report", number = "67", year = "1988", month = may, institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", note = "Revised October 1988", bibdate = "Sat Dec 30 09:54:08 1995", } @PhdThesis{int:Jarre7, author = "F. Jarre", title = "The method of analytic centers for smooth convex programs", year = "1989", school = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:54:10 1995", } @TechReport{int:Jarre8, author = "F. Jarre", title = "Interior--point methods for convex programming", type = "{Technical Report}", number = "SOL~90--16", year = "1990", institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @InCollection{int:Jarre9, author = "F. Jarre and G. Sonnevend and J. Stoer", title = "On the complexity of a numerical algorithm for solving generalized convex quadratic programs by following a central path", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "233--242", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Jarre10, author = "F. Jarre and M. A. Saunders", title = "An adaptive primal--dual method for linear programming", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "7--16", } @TechReport{int:Jensen1, author = "D. L. Jensen and A. E. Steger", title = "A variation of {Karmarkar}'s algorithm to solve linear programs in standard form", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles, CA, USA}", year = "1986", month = apr, institution = "State University of New York", address = "Stony Brook, NY~11794, USA", } @TechReport{int:Ji1, author = "J. Ji and F. Potra and R. A. Tapia and Y. Zhang", title = "An interior--point method with polynomial complexity and superlinear convergence for linear complementarity problems", type = "{Technical Report}", year = "1991", institution = "Dept.\ of Mathematics, The University of Iowa", address = "Iowa City, IA~52242, USA", note = "Technical Report TR--91--23, Dept.\ of Mathematical Sciences, Rice University, Houston, TX~77251, USA, 1991", } @TechReport{int:Jung1, author = "H. W. Jung and R. E. Marsten and M. J. Saltzman", title = "The column {Cholesky} method for numerical factorization in interior point algorithms", type = "{Technical Report}", number = "596", year = "1991", institution = "Dept.\ of Mathematical Sciences,Clemson University", address = "Clemson, SC, USA", } @TechReport{int:Kaeschel1, author = "J. K{\"a}schel", title = "Karmarkar--{\"a}hnliche {Verfahren in der Linearen Optimierung (Karmarkar--type procedures in linear programming)}", type = "{Talk held at the DGOR--Jahrestagung in Stuttgart--Hohenheim, Germany}", year = "1991", month = sep, institution = "Sektion Wirtschaftswissenschaften, TU Chemnitz", address = "P.~O.~Box~964, D-9010~Chemnitz, East Germany", bibdate = "Sat Dec 30 09:54:52 1995", } @Article{int:Kalantari1, author = "B. Kalantari", title = "Karmarkar's algorithm with improved steps", journal = "Mathematical Programming", volume = "46", year = "1990", pages = "73--78", } @TechReport{int:Kalantari2, author = "B. Kalantari", title = "Derivation of a generalized and strengthened {Gordan Theorem} from generalized {Karmarkar} potential and logarithmic barrier functions", type = "{Technical Report}", number = "LCSR--TR--121", year = "1989", institution = "Laboratory for Computer Science Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @InCollection{int:Kalantari3, author = "B. Kalantari", title = "Canonical problems for quadratic programming and projective methods for their solution", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "243--263", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Kalantari4, author = "B. Kalantari", title = "Solving linear programming by bisection and a projective feasibility algorithm", type = "{Technical Report}", number = "LCSR--TR--91", year = "1987", institution = "Laboratory for Computer Science Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Kalantari5, author = "B. Kalantari", title = "Generalization of {Karmarkar's} algorithm to convex homogeneous functions", type = "{Technical Report}", number = "LCSR--TR--130", year = "1989", institution = "Laboratory for Computer Science Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Kaliski1, author = "J. A. Kaliski and Y. Ye", title = "A decomposition variant of the potential reduction algorithm for linear programming", type = "{Working Paper}", year = "1991", institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @Article{int:Kaliski2, author = "J. A. Kaliski and Y. Ye", title = "Convergence behavior of {Karmarkar}'s projective algorithm for solving a simple linear program", journal = "Operations Research Letters", volume = "10", year = "1991", pages = "389--393", } @TechReport{int:Kallio1, author = "M. Kallio", title = "On gradient projection for linear programming", type = "Manuscript", year = "1986", institution = "School of Organization and Management, Yale University", address = "New Haven, CT~06520, USA", } @Article{int:Kallio2, author = "M. Kallio and E. L. Porteus", title = "A class of methods for linear programming", journal = "Mathematical Programming", volume = "14", year = "1978", pages = "161--176", } @Article{int:Kamath1, author = "A. P. Kamath and N. K. Karmarkar and K. G. Ramakrishnan and M. G. C. Resende", title = "Computational experience with an interior point algorithm on the satisfiability problem", journal = "Annals of Operations Research", volume = "25", year = "1990", pages = "43--58", } @Book{int:Kannan1, author = "R. Kannan and W. R. Pulleyblank", title = "Integer Programming and Combinatorial Optimization", year = "1990", publisher = "University of Waterloo Press", address = "Waterloo, Ontario, Canada", } @Article{int:Kapoor1, author = "S. Kapoor and P. M. Vaidya", title = "Fast algorithms for convex quadratic programming and multicommodity flows", journal = "Proceedings of the 18th Annual ACM Symposium on Theory of Computing", year = "1986", pages = "147--159", } @TechReport{int:Kapoor2, author = "S. Kapoor and P. M. Vaidya", title = "An extension of {Karmarkar}'s interior point method to convex quadratic programming", type = "{Technical Report}", year = "1988", institution = "Dept.\ of Computer Science, University of Illinois at Urbana--Champaign", address = "Urbana, IL~61820, USA", } @TechReport{int:Kapoor3, author = "S. Kapoor and P. M. Vaidya", title = "Speeding--up {Karmarkar}'s algorithm for multicommodity flows", type = "{Technical Report}", year = "1989", institution = "Dept.\ of Computer Science, University of Illinois at Urbana--Champaign", address = "Urbana, IL~61820, USA", note = "To appear in {\em Mathematical Programming}", } @Book{int:Karloff1, author = "H. Karloff", title = "Linear Programming", year = "1991", publisher = "Birkh{\"a}user Verlag", address = "Basel, Switzerland", note = "Chapter on Karmarkar's algorithm", } @Article{int:Karmarkar1, author = "N. K. Karmarkar", title = "A new polynomial--time algorithm for linear programming", journal = "Proceedings of the 16th Annual ACM Symposium on Theory of Computing", year = "1984", pages = "302--311", } @Article{int:Karmarkar2, author = "N. K. Karmarkar", title = "A new polynomial--time algorithm for linear programming", journal = "Combinatorica", volume = "4", year = "1984", pages = "373--395", } @TechReport{int:Karmarkar3, author = "N. K. Karmarkar", title = "Some comments on the significance of the new polynomial--time algorithm for linear programming", type = "{Technical Report}", year = "1984", institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Karmarkar4, author = "N. K. Karmarkar", title = "An interior--point approach to {NP}--complete problems", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1988", month = jul, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Misc{int:Karmarkar5, author = "N. K. Karmarkar", title = "Methods and apparatus for efficient resource allocation", howpublished = "U.S.~Patent No.~4.744.028", year = "1988", note = "AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA", } @InCollection{int:Karmarkar6, author = "N. K. Karmarkar", title = "Riemannian geometry underlying interior--point methods for linear programming", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "51--75", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Karmarkar7, author = "N. K. Karmarkar and K. G. Ramakrishnan", title = "Further developments in the new polynomial--time algorithm for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Boston, MA, USA}", year = "1985", month = may, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Karmarkar8, author = "N. K. Karmarkar and K. G. Ramakrishnan", title = "Implementation and computational aspects of the {Karmarkar} algorithm for linear programming, using an iterative method for computing projections", type = "{Talk held at the 13th International Symposium on Mathematical Programming in Tokyo, Japan}", year = "1988", month = aug, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", note = "Extended Abstract circulated at the Symposium", } @TechReport{int:Karmarkar9, author = "N. K. Karmarkar and K. G. Ramakrishnan", title = "Computational results of an interior point algorithm for large scale linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @TechReport{int:Karmarkar10, author = "N. K. Karmarkar and K. G. Ramakrishnan", title = "Robust control system models and their solution by the {Karmarkar} algorithm", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Karmarkar11, author = "N. K. Karmarkar and L. P. Sinha", title = "Application of {Karmarkar}'s algorithm to overseas telecommunications facilities planning", type = "{Talk held at the 12th International Symposium on Mathematical Programming in Boston, MA, USA}", year = "1985", month = aug, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Karmarkar12, author = "N. K. Karmarkar and K. G. Ramakrishnan and M. G. C. Resende", title = "An interior point algorithm for zero--one integer programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ 07974, USA", } @TechReport{int:Karmarkar13, author = "N. K. Karmarkar and K. G. Ramakrishnan and M. G. C. Resende", title = "Further developments on an interior point algorithm for zero--one integer programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Karmarkar14, author = "N. K. Karmarkar and J. C. Lagarias and L. Slutsman and P. Wang", title = "Power--series variants of {Karmarkar}--type algorithms", journal = "AT~\&~T Technical Journal", volume = "68", year = "1989", pages = "20--36", } @TechReport{int:Karmarkar15, author = "N. K. Karmarkar", title = "Interior point methods in optimization", type = "{Talk held at the Second International Conference on Industrial and Applied Mathematics (ICIAM~'91), Washington, DC, USA}", year = "1991", month = jul, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Karmarkar16, author = "N. K. Karmarkar", title = "Recent developments in new approaches to linear programming", type = "{Talk held at the SIAM Conference on Optimization, Houston, TX, USA}", year = "1987", institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Karmarkar17, author = "N. K. Karmarkar and K. G. Ramakrishnan and M. G. C. Resende", title = "An interior point algorithm to solve computationally difficult set covering problems", type = "{Extended Abstract}", year = "1989", institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @TechReport{int:Karmarkar18, author = "N. K. Karmarkar", title = "Why is the new algorithm better than simplex method and ellipsoid method~?", type = "{Extended Abstract}", year = "1984/85", institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @InCollection{int:Karmarkar19, author = "N. K. Karmarkar", title = "An interior--point approach to {NP}--complete problems -- {Part I}", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "297--308", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Karmarkar20, author = "N. K. Karmarkar and K. G. Ramakrishnan and M. G. C. Resende", title = "An interior--point approach to the maximum independent set problem in dense random graphs", type = "{Manuscript (in preparation)}", year = "1988/1990", institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Katsura1, author = "R. Katsura and M. Fukushima and T. Ibaraki", title = "Interior methods for nonlinear minimum cost network flow problems", journal = "Journal of the Operations Research Society of Japan", volume = "32", year = "1989", pages = "174--179", } @Article{int:Kennington1, author = "J. L. Kennington", title = "Using {KORBX} for military airlift applications", journal = "Proceedings of the 28th IEEE Conference on Decision and Control", year = "1989", month = dec, pages = "1603--1605", } @PhdThesis{int:Keraghel1, author = "A. Keraghel", title = "Etude adaptive et comparative des principales variantes dans l'algorithme de {Karmarkar}", year = "1989", school = "Laboratoire ARTEMIS (IMAG), Universite Joseph Fourier", address = "BP~68, F-38402 St.~Martin d'Heres Cedex, France", note = "(In French)", bibdate = "Thu Nov 21 08:26:23 1996", } @TechReport{int:Khachian1, author = "L. G. Khachian and M. J. Todd", title = "On the complexity of approximating the maximal inscribed ellipsoid for a polytope", type = "{Technical Report}", number = "893", year = "1990", institution = "School of Operations Research and Industrial Engineering, College of Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @Article{int:Kim1, author = "K. Kim and J. L. Nazareth", title = "The decomposition principle and algorithms for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "119--133", } @Article{int:Knyazev1, author = "E. A. Knyazev", title = "The method of centers with adaptation of parameters on the basis of the steepest descent", journal = "Issledovaniya po Prikladnoi Matematike (Kazanskii Universitet)", volume = "15", year = "1988", pages = "13--24", note = "(In Russian)", } @Article{int:Kojima1, author = "M. Kojima", title = "Determining basic variables of optimal solutions in {Karmarkar's new LP} algorithm", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "499--515", } @TechReport{int:Kojima2, author = "M. Kojima and K. Tone", title = "An efficient implementation of {Karmarkar's new LP} algorithm", type = "Research Reports on Information Sciences, Ser.~B~: Operations Research", number = "B--180", year = "1986", institution = "Dept.\ of Information Sciences, Tokyo Institute of Technology", address = "Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @TechReport{int:Kojima3, author = "M. Kojima and N. Megiddo and Y. Ye", title = "An interior point potential reduction algorithm for the linear complementarity problem", type = "{Technical Report}", number = "RJ~6486", year = "1988", institution = "IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", note = "To appear in {\em Mathematical Programming}", } @InCollection{int:Kojima4, author = "M. Kojima and S. Mizuno and A. Yoshise", title = "A primal--dual interior point algorithm for linear programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", editor = "N.~Megiddo", year = "1989", pages = "29--47", } @Article{int:Kojima5, author = "M. Kojima and S. Mizuno and A. Yoshise", title = "Ellipsoids that contain all the solutions of a positive semi--definite linear complementarity problems", journal = "Mathematical Programming", volume = "48", year = "1990", pages = "415--435", } @Article{int:Kojima6, author = "M. Kojima and S. Mizuno and A. Yoshise", title = "An ${O(\sqrt{n}L)}$ iteration potential reduction algorithm for linear complementarity problems", journal = "Mathematical Programming", volume = "50", year = "1991", pages = "331--342", } @Article{int:Kojima7, author = "M. Kojima and S. Mizuno and A. Yoshise", title = "A polynomial--time algorithm for a class of linear complementarity problems", journal = "Mathematical Programming", volume = "44", year = "1989", pages = "1--26", } @Book{int:Kojima8, author = "M. Kojima and N. Megiddo and T. Noma and A. Yoshise", title = "A unified approach to interior point algorithms for linear complementarity problems", year = "1991", series = "Lecture Notes in Computer Science", volume = "538", publisher = "Springer-Verlag", address = "Berlin, Germany", } @Article{int:Kojima9, author = "M. Kojima and N. Megiddo", title = "The relation between the path of centers and {Smale's} regularization of the linear programming problem", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "135--139", } @TechReport{int:Kojima10, author = "M. Kojima and Y. Kurita and S. Mizuno", title = "Large--step interior point algorithms for linear complementarity problems", type = "Research Reports on Information Sciences, Ser.~B~: Operations Research", number = "B--243", year = "1991", institution = "Dept.\ of Information Sciences, Tokyo Institute of Technology", address = "Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @TechReport{int:Kojima11, author = "M. Kojima and N. Megiddo and S. Mizuno", title = "A general framework of continuation methods for complementarity problems", type = "{Research Report}", number = "RJ~7720~(71585)", year = "1990", institution = "IBM Almaden Research Division", address = "San Jose, CA~95120-6099, USA", } @TechReport{int:Kojima12, author = "M. Kojima and N. Megiddo and S. Mizuno", title = "Theoretical convergence of large--step--primal--dual interior point algorithms for linear programming", type = "{Research Report}", number = "RJ~7872~(72532)", year = "1990", institution = "IBM Almaden Research Division", address = "San Jose, CA~95120-6099, USA", note = "To appear in {\em Mathematical Programming}", } @Article{int:Kojima13, author = "M. Kojima and S. Mizuno and T. Noma", title = "A new continuation method for complementarity problems with uniform {$P$}--functions", journal = "Mathematical Programming", volume = "43", year = "1989", pages = "107--113", } @TechReport{int:Kojima14, author = "M. Kojima and S. Mizuno and A. Yoshise", title = "A little theorem of the {$Big-M$} in interior point algorithms", type = "Research Reports on Information Sciences, Ser.~B~: Operations Research", number = "B--239", year = "1991", month = feb, institution = "Dept.\ of Information Sciences, Tokyo Institute of Technology", address = "Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @Article{int:Kojima15, author = "M. Kojima and N. Megiddo and T. Noma and A. Yoshise", title = "A unified approach to interior point algorithms for linear complementarity problems~: {A} summary", journal = "Operations Research Letters", volume = "10", year = "1991", pages = "247--254", } @Article{int:Kojima16, author = "M. Kojima and S. Mizuno and T. Noma", title = "Limiting behavior of trajectories by a continuation method for monotone complementarity problems", journal = "Mathematics of Operations Research", volume = "15", number = "4", year = "1990", pages = "662--675", } @TechReport{int:Kojima17, author = "M. Kojima and N. Megiddo and T. Noma", title = "Homotopy continuation methods for complementarity problems", type = "{Research Report}", number = "RJ~6638~(63949)", year = "1989", institution = "IBM Almaden Research Division", address = "San Jose, CA~95120-6099, USA", } @TechReport{int:Kojima18, author = "M. Kojima and N. Megiddo and T. Noma", title = "Homotopy continuation methods for nonlinear complementarity problems", type = "{Research Report}", year = "1989", institution = "IBM Almaden Research Division", address = "San Jose, CA~95120-6099, USA", } @Article{int:Kolata1, author = "G. Kolata", title = "A fast way to solve hard problems", journal = "Science", volume = "225", year = "1984", month = sep, pages = "1379--1380", } @TechReport{int:Konno1, author = "H. Konno and Y. Yajima", title = "Path--following algorithms for solving nonconvex programming problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Institute of Human and Social Science, Institute of Technology", address = "2-12-1~Oh-Okayama, Meguro-ku, Tokyo 152, Japan", } @Article{int:Konno2, author = "H. Konno", title = "Recent advances in linear programming", journal = "Journal of the Japan Society of Simulation Technology", volume = "6", number = "1", year = "1987", month = mar, pages = "18--26", note = "(In Japanese)", } @TechReport{int:Kortanek1, author = "K. O. Kortanek", title = "Vector--supercomputer experiments with the linear programming scaling algorithm", type = "{Working Paper Series}", number = "87--2", year = "1987", institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", note = "To appear in {\em SIAM Journal on Scientific and Statistical Computations (1991~?)}", } @TechReport{int:Kortanek2, author = "K. O. Kortanek", title = "A second order affine scaling algorithm for the geometric programming dual with logarithmic barrier", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @Article{int:Kortanek3, author = "K. O. Kortanek and M. Shi", title = "Convergence results and numerical experiments on a linear programming hybrid algorithm", journal = "European Journal of Operational Research", volume = "32", year = "1987", pages = "47--61", } @Article{int:Kortanek4, author = "K. O. Kortanek and J. Zhu", title = "New purification algorithms for linear programming", journal = "Naval Research Logistics Quarterly", volume = "35", year = "1988", pages = "571--583", } @TechReport{int:Kortanek5, author = "K. O. Kortanek and D. N. Leo and M. Shi", title = "An application of a hybrid algorithm for semi--infinite programming", type = "{Talk held at the 12th Symposium on Mathematical Programming, Cambridge, MA, USA}", year = "1985", institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @Article{int:Kortanek6, author = "K. O. Kortanek and F. Potra and Y. Ye", title = "On some efficient interior point methods for nonlinear convex programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "169--189", } @TechReport{int:Kortanek7, author = "K. O. Kortanek and H. No", title = "A second order affine scaling algorithm for the geometric programming dual with logarithmic barrier", type = "{Working Paper Series}", number = "90--07", year = "1990", institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @TechReport{int:Kortanek8, author = "K. O. Kortanek and J. Zhu", title = "Controlling the parameter in the logarithmic barrier term for convex programming problems", type = "{Working Paper Series}", number = "90--12", year = "1990", institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @TechReport{int:Kortanek9, author = "K. O. Kortanek and S. Huang and J. Zhu", title = "Central path trajectories and controlled dual perturbations for geometric programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Management Science, College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @Article{int:Korytowski1, author = "A. Korytowski", title = "Inner search methods for linear programming", journal = "Zastosowania Matematyki (Warshaw, Poland)", volume = "20", number = "2", year = "1990", pages = "307--327", } @TechReport{int:Kovacevic1, author = "V. V. {Kovacevic--Vujcic}", title = "Improving the rate of convergence of interior point methods for linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "University of Belgrade", address = "Belgrade, Yugoslavia", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @Article{int:Kozlov1, author = "A. Kozlov", title = "The {Karmarkar} algorithm~: {Is} it for real~?", journal = "SIAM News", volume = "18", number = "6", year = "1985", month = nov, pages = "1, 4, 13", } @Article{int:Kozlov2, author = "A. Kozlov and L. W. Black", title = "Berkeley obtains new results with {Karmarkar} algorithm", journal = "SIAM News", volume = "19", number = "3", year = "1986", month = may, pages = "3, 20", } @TechReport{int:Kranich1, author = "E. Kranich", title = "Interior point methods for mathematical programming~: {A} bibliography", type = "{Discussion Paper}", number = "171", year = "1991", month = may, institution = "Institute of Economy and Operations Research, FernUniversit{\"a}t Hagen", address = "P.O. Box~940, D-5800~Hagen~1, Germany", note = "{The (actual) bibliography can be accessed electronically by sending e--mail to `{\em netlib@research.bell-labs.com}' with message `{\em send index from bib}'}", bibdate = "Sat Dec 30 09:54:16 1995", } @TechReport{int:Lagarias1, author = "J. C. Lagarias", title = "Analytic algorithms for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New Orleans, USA}", year = "1987", month = may, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Lagarias2, author = "J. C. Lagarias", title = "The nonlinear geometry of linear programming, {Part~III}~: {Projective Legrende} transform coordinates and {Hilbert} geometry", journal = "Transactions of the American Mathematical Society", volume = "320", year = "1990", pages = "193--225", } @Book{int:Lagarias3, author = "J. C. Lagarias and M. J. Todd", title = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, {USA}, June/July 1988", year = "1990", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Lasdon1, author = "L. S. Lasdon and J. C. Plummer and G. Yu", title = "An interior point algorithm for general nonlinear programs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "MSIS Department, College of Business Administration, University of Texas at Austin", address = "Austin, TX~78712, USA", } @TechReport{int:Lawler1, author = "E. L. Lawler", title = "Is {Karmarkar}'s algorithm for real~?", type = "{Talk held at the EURO VII Congress on Operations Research in Bologna, Italy}", year = "1985", month = jun, institution = "University of California", address = "Berkeley, CA~94720, USA", } @TechReport{int:Levkovitz1, author = "R. Levkovitz and G. Mitra and M. Tamiz", title = "Integration of the interior point method within simplex~: {Experiments} in feasible basis recovery", type = "{Technical Report}", year = "1991", institution = "Dept.\ of Mathematics and Statistics, Brunel University", address = "Uxbridge, Middlesex~UB8~3PH, UK", } @TechReport{int:Lindfield1, author = "G. R. Lindfield and A. Salhi", title = "A comparative study of the performance and implementation of the {Karmarkar} algorithm", type = "{Talk held at the Martin Beale Memorial Symposium in London, UK}", year = "1987", month = jul, institution = "Dept.\ of Computer Science and Applied Mathematics, Aston University", address = "Birmingham B4~7ET, Great Britain", } @Article{int:Lisser1, author = "A. Lisser and P. Tolla", title = "Variants of {Karmarkar}'s algorithm", journal = "Electricite de France (EDF) Bulletin de la Direction des Etudes et Recherches Serie C Mathematique, Informatique (Paris)", volume = "3", year = "1989", pages = "21--36", } @TechReport{int:Lisser2, author = "A. Lisser and N. Maculan and M. Minoux", title = "Approximate one--dimensional minimization of the potential function improves the convergence speed of {Karmarkar}'s method", type = "{Unpublished Manuscript}", year = "1985", institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @TechReport{int:Lisser3, author = "A. Lisser and N. Maculan and M. Minoux", title = "Large steps preserving polynomiality in {Karmarkar}'s algorithm", type = "Cahier", number = "77", year = "1987", institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @TechReport{int:Lisser4, author = "A. Lisser and M. J. Chifflet", title = "A comparison of projective and affine approaches in interior point methods", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Centre National d'Etudes des Telecommunications, PAA--ATR", address = "38-40~Rue du General-Leclerc, F-92131~Issy-Les-Moulineaux, France", } @TechReport{int:Lisser5, author = "A. Lisser and P. Tolla", title = "An efficient software using the {Karmarkar}'s algorithm", type = "{Talk held at the EURO/TIMS Joint International Conference on Operational Research in Paris, France}", year = "1988", month = jul, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @PhdThesis{int:Lisser6, author = "A. Lisser", title = "Un logiciel derive de l'algorithme de {Karmarkar} pour la resolution de programmes lineaires de grande taille {(A computational derivation of Karmarkar's algorithm for the solution of large--scaled linear programs)}", year = "1987", school = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", note = "(In French)", } @TechReport{int:Liu1, author = "S. Liu", title = "A long step path--following algorithm for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Liu2, author = "S. Liu and D. Goldfarb", title = "Interior point potential function reduction algorithms for solving convex quadratic programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @Book{int:Lootsma1, author = "F. A. Lootsma", title = "Numerical Methods for Nonlinear Optimization", publisher = "Academic Press", year = "1972", address = "London, UK", } @Article{int:Luss1, author = "H. Luss", title = "Optimization~: {Methodolgy}, algorithms and applications", journal = "AT~\&~T Technical Journal", volume = "68", year = "1989", pages = "3--6", } @TechReport{int:Lustig1, author = "I. J. Lustig", title = "A practical approach to {Karmarkar}'s algorithm", type = "{Technical Report}", number = "SOL~85--5", year = "1985", month = jun, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Lustig2, author = "I. J. Lustig", title = "Identifying an optimal basis of a linear program using an interior point method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Lustig3, author = "I. J. Lustig", title = "A generic primal--dual interior point algorithm", type = "{Technical Report}", number = "SOR~88--3", year = "1988", institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Lustig4, author = "I. J. Lustig", title = "An experimental analysis of the convergence rate of an interior point algorithm", type = "{Technical Report}", number = "SOR~88--5", year = "1988", month = mar, institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @Article{int:Lustig5, author = "I. J. Lustig", title = "Feasibility issues in an interior point method for linear programming", journal = "Mathematical Programming", volume = "49", year = "1990/91", pages = "145--162", } @Article{int:Lustig6, author = "I. J. Lustig", title = "An analysis of an available set of linear programming test problems", journal = "Computers and Operations Research", volume = "16", year = "1989", pages = "173--184", note = "Augmented version in the Technical Report SOL~87-11, Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University, Stanford, CA~94305, USA, 1987", } @Article{int:Lustig7, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "Computational experience with a primal--dual interior point method for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "191--222", } @TechReport{int:Lustig8, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "Recent computational experience with the primal--dual interior point method for linear programming", type = "{Technical Report}", number = "RRR~46--89", year = "1990", institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @Article{int:Lustig9, author = "I. J. Lustig and J. M. Mulvey and T. J. Carpenter", title = "The formulation of stochastic programs for interior point methods", journal = "Operations Research", volume = "39", number = "5", year = "1991", pages = "757--770", } @TechReport{int:Lustig10, author = "I. J. Lustig and D. F. Shanno and J. W. Gregory", title = "The primal--dual interior point method on a {Cray} supercomputer", type = "{Technical Report}", number = "SOR~89--21", year = "1989", institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Lustig11, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "Recent advances in the {OB1} interior point code", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @InCollection{int:Lustig12, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "The primal--dual interior point method on the {Cray} supercomputer", booktitle = "Large--Scale Numerical Optimization, Papers from the Workshop held at Cornell University, Ithaca, NY, USA, October 1989", series = "SIAM Proceedings in Applied Mathematics", volume = "46", year = "1990", pages = "70--80", editor = "T. F. Coleman and Y. Li", publisher = "Society of Industrial and Applied Mathematics (SIAM)", address = "Philadelphia, PA, USA", } @TechReport{int:Lustig13, author = "I. J. Lustig", title = "An implementation of a strongly polynomial time algorithm for basis recovery", type = "{Technical Report}", number = "(in preparation)", year = "1991", institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Lustig14, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "On implementing {Mehrotra}'s predictor--corrector interior point method for linear programming", type = "{Technical Report}", number = "SOR~90--03", year = "1990", month = apr, institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", note = "To appear in {\em SIAM Journal on Optimization}", } @TechReport{int:Lustig15, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "Starting and restarting the primal--dual interior point method", type = "{Technical Report}", number = "SOR~90--14", year = "1990", institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Lustig16, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "The interaction of algorithms and architectures for interior point methods", type = "{Technical Report}", number = "SOR~91--18", year = "1991", month = jul, institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @InCollection{int:Lustig17, author = "I. J. Lustig", title = "Phase~1 search directions for a primal--dual interior point method for linear programming", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "121--130", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Lustig18, author = "I. J. Lustig and R. E. Marsten and D. F. Shanno", title = "Interior method vs.\ simplex method~: {Beyond} {\em netlib}", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "41--44", } @MastersThesis{int:Maier1, author = "S. Maier", title = "{Primal--duales innere--Punkte--Verfahren mit endlicher Genauigkeit zur L{\"o}sung linearer Programme (A primal--dual interior point method with finite accuracy for solving linear programs)}", year = "1989", school = "Institut f{\"u}r Mathematik der Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Augsburg", address = "D-8900~Augsburg, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:54:20 1995", } @TechReport{int:Mangasarian1, author = "O. L. Mangasarian and R. Setiono", title = "Serial and parallel interior proximal point methods for linear programs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @MastersThesis{int:Margraff1, author = "G. Margraff", title = "{Analyse und Modifikation des Karmarkar Verfahrens (Analysis and modification of Karmarkar's algorithm)}", year = "1987", school = "Universit{\"a}t Trier, Fachbereich~IV", address = "D-5500~Trier, Germany", note = "(In German)", bibdate = "Sat Dec 30 09:54:23 1995", } @TechReport{int:Marsten1, author = "R. E. Marsten and M. J. Saltzman", title = "A dual--affine interior point algorithm for {LP's} with bounded variables", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "Dept.\ of MIS, University of Arizona", address = "Tucson, AZ~85721, USA", } @TechReport{int:Marsten2, author = "R. E. Marsten and D. F. Shanno", title = "On implementing {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1985", institution = "Dept.\ of MIS, University of Arizona", address = "Tucson, AZ~85721, USA", } @TechReport{int:Marsten3, author = "R. E. Marsten and D. F. Shanno", title = "Recent computational experience with the primal--dual interior point method", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "School of Industrial and Systems Engineering, Georgia Technology Institute", address = "Atlanta, GA~30322-0205, USA", } @TechReport{int:Marsten4, author = "R. E. Marsten and M. J. Saltzman and J. W. Gregory and T. G. Hewitt and D. F. Shanno", title = "The dual affine interior point method for linear programming implementation on {Cray} supercomputers", type = "{Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver, British Columbia, Canada}", year = "1989", month = may, institution = "School of Industrial and Systems Engineering, Georgia Technology Institute", address = "Atlanta, GA~30322-0205, USA", } @Article{int:Marsten5, author = "R. E. Marsten and M. J. Saltzman and D. F. Shanno and J. F. Ballintijn and G. S. Pierce", title = "Implementation of a dual affine interior point algorithm for linear programming", journal = "ORSA Journal on Computing", volume = "1", year = "1989", pages = "287--297", } @Article{int:Marsten6, author = "R. E. Marsten and R. Subramaniam and M. J. Saltzman and I. J. Lustig and D. F. Shanno", title = "Interior point methods for linear programming~: {Just call Newton, Lagrange, and Fiacco and McCormick~!}", journal = "Interfaces", volume = "20", number = "4", year = "1990", pages = "105--116", } @TechReport{int:Marsten7, author = "R. E. Marsten", title = "The {IMP System} on personal computers", type = "{Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis, USA}", year = "1987", month = oct, institution = "Dept.\ of MIS, University of Arizona", address = "Tucson, AZ~85721, USA", } @TechReport{int:Marsten8, author = "R. E. Marsten", title = "Interior point methods for large scale linear programming", type = "{Talk held at the Second International Conference on Industrial and Applied Mathematics (ICIAM~'91), Washington, DC, USA}", year = "1991", month = jul, institution = "School of Industrial and Systems Engineering, Georgia Technology Institute", address = "Atlanta, GA~30322-0205, USA", } @TechReport{int:Marsten9, author = "R. E. Marsten and D. F. Shanno", title = "Interior point methods for linear programming~: {Ready} for production use", type = "{Workshop at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "School of Industrial and System Engineering, Georgia Institute of Technology", address = "Atlanta, GA~30322, USA", } @TechReport{int:Martinhon1, author = "C. Martinhon and C. C. Gonzaga", title = "A unified analysis of affine and projective primal potential reduction algorithms for linear programming", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Dept.\ of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro", address = "21941~Rio~de~Janeiro, RJ, Brazil", } @TechReport{int:Marxen1, author = "A. Marxen", title = "Primal barrier methods for linear programming", type = "{Technical Report}", number = "SOL~89--6", year = "1989", month = jun, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @PhdThesis{int:Marxen2, author = "A. Marxen", title = "Primal barrier methods for linear programming", year = "1989", school = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Masuzawa1, author = "K. Masuzawa and S. Mizuno and M. Mori", title = "A polynomial time interior point algorithm for minimum cost flow problems", journal = "Journal of the Operations Research Society of Japan", volume = "33", year = "1990", pages = "157--167", } @Article{int:McDiarmid1, author = "C. McDiarmid", title = "On the improvement per iteration in {Karmarkar}'s method for linear programming", journal = "Mathematical Programming", volume = "46", year = "1990", pages = "299--320", } @TechReport{int:McDiarmid2, author = "C. McDiarmid", title = "Why {Karmarkar}'s method is fast~?", type = "{Talk held at the EURO/TIMS Joint International Conference on Operational Research in Paris, France}", year = "1988", month = jul, institution = "Institute of Economics and Statistics, St. Cross Building, Oxford University", address = "Oxford~OX1~3UL, UK", } @Article{int:McQueen1, author = "J. F. McQueen", title = "Symposium on {Karmarkar}'s algorithm and related algorithms for linear programming", journal = "Bulletin of the Institute of Mathematics and Its Applications", volume = "21", year = "1985", pages = "154--155", } @Article{int:McShane1, author = "K. A. McShane and C. L. Monma and D. F. Shanno", title = "An implementation of a primal--dual interior point method for linear programming", journal = "ORSA Journal on Computing", volume = "1", year = "1989", pages = "70--83", } @TechReport{int:McShane2, author = "K. A. McShane", title = "A superlinearly convergent ${O(\sqrt{n}L)}$ iteration primal--dual linear programming algorithm", type = "Manuscript", year = "1991", address = "2537~Villanova Drive, Vienna, Virginia, USA", } @TechReport{int:Megiddo1, author = "N. Megiddo", title = "A variation on {Karmarkar}'s algorithm", type = "{Preliminary Report}", year = "1985", institution = "IBM Research Division, Almaden Research Center", address = "San Jose, CA~95120-6099, USA", } @Book{int:Megiddo2, author = "N. Megiddo", title = "New Approaches to Linear Programming", year = "1986", series = "Algorithmica", volume = "1(4)", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:25 1995", } @Article{int:Megiddo3, author = "N. Megiddo", title = "Introduction~: {New} approaches to linear programming", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "387--394", } @Article{int:Megiddo4, author = "N. Megiddo", title = "Linear programming~(1986)", journal = "Annual Review of Computer Science", volume = "2", year = "1987", pages = "119--145", } @TechReport{int:Megiddo5, author = "N. Megiddo", title = "Report on the conference~: {Progress} in mathematical programming", type = "{Technical Report}", number = "RJ~5923", year = "1987", month = oct, institution = "IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @InCollection{int:Megiddo6, author = "N. Megiddo", title = "On the complexity of linear programming", booktitle = "Advances in Economic Theory---The Fifth World Congress", series = "Econometric Society Monographs", volume = "12", publisher = "Cambridge University Press", address = "Cambridge, UK", editor = "T. F. Bewley", year = "1987", pages = "225--258", } @InCollection{int:Megiddo7, author = "N. Megiddo", title = "On solving the linear programming problem approximately", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "35--50", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Megiddo8, author = "N. Megiddo", title = "Switching from a primal--dual {Newton} algorithm to a primal--dual (interior) simplex algorithm", type = "{Technical Report}", number = "RJ~6327", year = "1988", institution = "IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @Article{int:Megiddo9, author = "N. Megiddo", title = "On finding primal-- and dual--optimal bases", journal = "ORSA Journal on Computing", volume = "3", year = "1991", pages = "63--65", } @Book{int:Megiddo10, author = "N. Megiddo", title = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", year = "1989", } @InCollection{int:Megiddo11, author = "N. Megiddo", title = "Pathways to the optimal set in linear programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", editor = "N. Megiddo", year = "1989", pages = "131--158", publisher = "Springer-Verlag", address = "New York, NY, USA", note = "Identical version in~: {\em Proceedings of the 6th Mathematical Programming Symposium of Japan, Nagoya, Japan}, pages 1--35, 1986", } @Article{int:Megiddo12, author = "N. Megiddo and M. Shub", title = "Boundary behavior of interior point algorithms in linear programming", journal = "Mathematics of Operations Research", volume = "14", year = "1987", pages = "97--114", } @TechReport{int:Mehrotra1, author = "S. Mehrotra", title = "A self--correcting version of {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1986", institution = "Dept.\ of Industrial Engineering and Operations Research", address = "Columbia University, New York, NY~10027, USA", } @PhdThesis{int:Mehrotra2, author = "S. Mehrotra", title = "Variants of {Karmarkar}'s algorithm~: {Theoretical} complexity and practical implementation", year = "1987", school = "Dept.\ of Industrial Engineering and Operations Reseach, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Mehrotra3, author = "S. Mehrotra", title = "Implementation of some interior point methods for linear programming~: {Recent} developments", type = "{Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis, USA}", year = "1987", month = oct, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra4, author = "S. Mehrotra", title = "On implementation of interior point methods for linear programming~: {Karmarkar}'s preconditioners", type = "{Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver, British Columbia, Canada}", year = "1989", month = may, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra5, author = "S. Mehrotra", title = "Implementation of affine scaling methods~: {Approximate} solutions of systems of linear equations using preconditioned conjugate gradient methods", type = "{Technical Report}", number = "89--04", month = aug, year = "1989", institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra6, author = "S. Mehrotra", title = "Implementation of affine scaling methods~: {Towards} faster implementations with complete {Cholesky} factor in use", type = "{Technical Report}", number = "89--15", year = "1989", month = oct, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @Article{int:Mehrotra7, author = "S. Mehrotra", title = "On finding a vertex solution using interior point methods", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "233--253", } @TechReport{int:Mehrotra8, author = "S. Mehrotra", title = "On an implementation of the primal--dual predictor--corrector algorithms", type = "{Talk held at the Second Asilomar Workshop on Progress in Mathematical Programming, Asilomar, CA, USA}", year = "1990", month = feb, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra9, author = "S. Mehrotra", title = "Implementations of affine scaling methods~: {Speeding} up the computation", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra10, author = "S. Mehrotra", title = "On the implementation of a (primal--dual) interior point method", type = "{Technical Report}", number = "90--03", year = "1990", month = mar, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", note = "Revised June 1990", } @Article{int:Mehrotra11, author = "S. Mehrotra and J. Sun", title = "A method of analytic centers for quadratically constrained convex quadratic programs", journal = "SIAM Journal on Numerical Analysis", volume = "28", number = "2", year = "1991", pages = "529--544", } @InCollection{int:Mehrotra12, author = "S. Mehrotra and J. Sun", title = "An interior point algorithm for solving smooth convex programs based on {Newton}'s method", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "265--284", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Mehrotra13, author = "S. Mehrotra and J. Sun", title = "On computing the center of a quadratically constrained set", journal = "Mathematical Programming", volume = "50", year = "1991", pages = "81--89", } @Article{int:Mehrotra14, author = "S. Mehrotra and J. Sun", title = "An algorithm for convex quadratic programming that requires ${O(n^{3.5}L)}$ arithmetic operations", journal = "Mathematics of Operations Research", volume = "15", year = "1990", pages = "342--363", } @TechReport{int:Mehrotra15, author = "S. Mehrotra and J. Sun", title = "Path--following methods for convex programming", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra16, author = "S. Mehrotra", title = "Generalized prediction--corrector methods for solving linear programs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra17, author = "S. Mehrotra", title = "Higher--order methods for solving linear programs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra18, author = "S. Mehrotra", title = "Handling free variables in interior methods", type = "{Technical Report}", number = "91--06", year = "1991", month = mar, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra19, author = "S. Mehrotra", title = "Finite termination and superlinear convergence in primal--dual methods", type = "{Technical Report}", number = "91--13", year = "1991", month = jul, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra20, author = "S. Mehrotra", title = "Higher order methods and their performance", type = "{Technical Report}", number = "TR~90--16R1", year = "1990", institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", note = "Revised July 1991", } @TechReport{int:Mehrotra21, author = "S. Mehrotra and Y. Ye", title = "On finding the optimal facet of linear programs", type = "{Technical Report}", number = "TR~91--10", year = "1991", institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Mehrotra22, author = "S. Mehrotra", title = "Deferred rank--one updates in ${O(n^{3}L)}$ interior point algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @TechReport{int:Meketon1, author = "M. S. Meketon and R. J. Vanderbei", title = "Degeneracy issues in the affine scaling algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis, USA}", year = "1987", month = oct, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @InCollection{int:Meketon2, author = "M. S. Meketon", title = "Optimization in simulation~: {A} survey of recent results", booktitle = "Proceedings of the Winter Simulation Conference held in Atlanta, GA~30322, USA,December 1987", editor = "A. Thesen and H. Grant and W. D. Kelton", year = "1987", pages = "58--67", publisher = "ACM Press", address = "New York, NY, USA", } @TechReport{int:Meketon3, author = "M. S. Meketon", title = "Least absolute value regression", type = "{Working Paper}", year = "1985", institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Mennicken1, author = "J. Mennicken", title = "Implementation of a first order central path following algorithm for solving large linear programs", type = "{Technical Report}", number = "202", year = "1990", institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:54:26 1995", } @TechReport{int:Meyer1, author = "R. R. Meyer and G. L. Schultz", title = "Structured interior point methods for multicommodity flows", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @InCollection{int:Miagen1, author = "S. Miagen and T. Miyazaki", title = "Implementation and numerical experiments on an interior--point algorithm for linear programming", booktitle = "Proceedings of the InfoJapan~'90\ : Information Technology Harmonizing with Society, Tokyo, Japan, Oct.\ 1990", volume = "1", year = "1990", pages = "19--25", publisher = "North Holland", address = "Amsterdam, The Netherlands", } @TechReport{int:Minoux1, author = "M. Minoux", title = "New suggested implementation of {Karmarkar}'s algorithm", type = "Cahier", number = "71", year = "1986", month = may, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @PhdThesis{int:Mitchell1, author = "J. E. Mitchell", title = "Karmarkar's algorithm and combinatorial optimization problems", year = "1988", school = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853-7501, USA", } @InCollection{int:Mitchell2, author = "J. E. Mitchell and M. J. Todd", title = "On the relationship between the search directions in the affine and projective variants of {Karmarkar}'s linear programming algorithm", booktitle = "Contributions to Operations Research and Economics~: The Twentieth Anniversary of CORE", editor = "B. Cornet and H. Tulkens", year = "1989", pages = "237--250", publisher = "M.I.T. Press", address = "Cambridge, MA, USA", } @TechReport{int:Mitchell3, author = "J. E. Mitchell and M. J. Todd", title = "Solving linear ordering problems using {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1988", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853-7501, USA", } @Article{int:Mitchell4, author = "J. E. Mitchell and M. J. Todd", title = "A variant of {Karmarkar}'s linear programming algorithm for problems with some unrestricted variables", journal = "SIAM Journal on Matrix Analysis and Applications", volume = "10", year = "1989", pages = "30--38", } @TechReport{int:Mitchell5, author = "J. E. Mitchell and M. J. Todd", title = "Solving combinatorial optimization problems using {Karmarkar}'s algorithm, {Part~I}~: {Theory}", type = "{Technical Report}", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853-7501, USA", } @TechReport{int:Mitchell6, author = "J. E. Mitchell and M. J. Todd", title = "Solving combinatorial optimization problems using {Karmarkar}'s algorithm, {Part~II}~: {Computational} results", type = "{Technical Report}", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853-7501, USA", } @TechReport{int:Mitchell7, author = "J. E. Mitchell and M. J. Todd", title = "Solving perfect matching problems using {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1988", institution = "Rensselaer Polytechnic Institute, Dept.\ of Mathematical Sciences", address = "Troy, NY~12180-3590, USA", } @TechReport{int:Mitchell8, author = "J. E. Mitchell", title = "An interior point column generation method for linear programming with shifted barriers", type = "{RPI Technical Report}", number = "191", year = "1988", institution = "Rensselaer Polytechnic Institute, Dept.\ of Mathematical Sciences", address = "Troy, NY~12180-3590, USA", } @TechReport{int:Mitchell9, author = "J. E. Mitchell and M. J. Todd", title = "Solving combinatorial optimization problems using {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1990", month = may, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853-7501, USA", note = "Revised February 1991", } @InCollection{int:Mitchell10, author = "J. E. Mitchell and M. J. Todd", title = "Solving matching problems using {Karmarkar}'s algorithm", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "309--318", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Mitchell11, author = "J. E. Mitchell", title = "A note on updating lower bounds when using {Karmarkar}'s projective algorithm for linear programming", type = "{RPI Technical Report}", number = "190", year = "1990", institution = "Rensselaer Polytechnic Institute, Dept.\ of Mathematical Sciences", address = "Troy, NY~12180-3590, USA", } @TechReport{int:Mitchell12, author = "J. E. Mitchell and M. J. Todd", title = "Two variants of {Karmarkar}'s linear programming algorithm for problems with some unrestricted variables", type = "{Technical Report}", number = "741", year = "1987", month = "", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853-7501, USA", } @TechReport{int:Mitchell13, author = "J. E. Mitchell", title = "An interior point column generation method for linear programming using shifted barriers", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Rensselaer Polytechnic Institute, Dept.\ of Mathematical Sciences", address = "Troy, NY~12180-3590, USA", } @InCollection{int:Mitra1, author = "G. Mitra and M. Tamiz and J. Yadegar", title = "A hybrid algorithm for linear programming", booktitle = "Simulation and Optimization of Large Systems", editor = "A. J. Osiadacz", year = "1988", pages = "143--159", series = "The Institute of Mathematics and Its Applications Conference Series", volume = "13", publisher = "Clarendon Press", address = "Oxford, UK", } @Article{int:Mitra2, author = "G. Mitra and M. Tamiz and J. Yadegar", title = "Experimental investigation of an interior search method within a simplex framework", journal = "Communications of the ACM", volume = "31", number = "12", year = "1988", pages = "1474--1482", } @Article{int:Mizuno1, author = "S. Mizuno", title = "An ${O(n^{3}L)}$ algorithm using a sequence for linear complementarity problems", journal = "Journal of the Operations Research Society of Japan", volume = "33", year = "1990", pages = "66--75", } @Article{int:Mizuno2, author = "S. Mizuno", title = "A rank--one updating interior algorithm for linear programming", journal = "Arabian Journal for Science and Engineering", volume = "15", number = "4", year = "1990", pages = "671--677", } @Article{int:Mizuno3, author = "S. Mizuno and K. Masuzawa", title = "Polynomial time interior point algorithms for transportation problems", journal = "Journal of the Operations Research Society of Japan", volume = "32", year = "1989", pages = "371--382", } @TechReport{int:Mizuno4, author = "S. Mizuno and M. J. Todd and Y. Ye", title = "Anticipated behavior of path--following algorithms for linear programming", type = "{Technical Report}", number = "878", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Mizuno5, author = "S. Mizuno and M. J. Todd and Y. Ye", title = "Anticipated behavior of long--step algorithms for linear programming", type = "{Technical Report}", number = "882", year = "1990", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Mizuno6, author = "S. Mizuno and M. J. Todd and Y. Ye", title = "Anticipated behavior of interior point algorithms for linear programming", type = "{Technical Report}", year = "1990", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @Article{int:Mizuno7, author = "S. Mizuno and A. Yoshise and T. Kikuchi", title = "Practical polynomial time algorithms for linear complementarity problems", journal = "Journal of the Operations Research Society of Japan", volume = "32", year = "1989", pages = "75--92", } @TechReport{int:Mizuno8, author = "S. Mizuno and M. J. Todd and Y. Ye", title = "On adaptive step primal--dual interior--point algorithms for linear programming", type = "{Technical Report}", number = "944", year = "1990", month = oct, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "To appear in {\em Mathematics of Operations Research}", } @TechReport{int:Mizuno9, author = "S. Mizuno", title = "A new polynomial time method for a linear complementarity problem", type = "{Technical Report}", number = "16", year = "1989", institution = "Dept.\ of Management Science and Engineering, Tokyo Institute of Technology", address = "Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @Article{int:Mizuno10, author = "S. Mizuno", title = "{$O(n^{\rho}L)$} iteration {$O(n^{3}L)$} potential reduction algorithms for linear programming", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "155--168", } @TechReport{int:Mizuno11, author = "S. Mizuno and M. J. Todd", title = "An {$O(n^{3}L)$} long step path following algorithm for a linear complementarity problem", type = "{Technical Report}", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "To appear in {\em Mathematical Programming}", } @TechReport{int:Mizuno12, author = "S. Mizuno and M. J. Todd and Y. Ye", title = "Anticipated behavior of long step algorithms for linear programming", type = "{Technical Report}", number = "24", year = "1989", institution = "Dept.\ of Management Science and Engineering, Tokyo Institute of Technology", address = "Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @TechReport{int:Mizuno13, author = "S. Mizuno and M. J. Todd", title = "An {$O(n^{3}L)$} adaptive path following algorithm for a linear complementarity problem", type = "{Technical Report}", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", } @TechReport{int:Monma1, author = "C. L. Monma", title = "Recent breakthroughs in linear programming methods", type = "{Internal Memorandum}", year = "1987", institution = "Bell Communications Research", address = "Morristown, NJ~07960, USA", } @Article{int:Monma2, author = "C. L. Monma", title = "Successful implementations of interior algorithms", journal = "SIAM News", volume = "22", number = "2", year = "1989", month = mar, pages = "14--16", } @Article{int:Monma3, author = "C. L. Monma and A. J. Morton", title = "Computational experience with the dual affine variant of {Karmarkar}'s method for linear programming", journal = "Operations Research Letters", volume = "6", year = "1987", pages = "261--267", } @TechReport{int:Monteiro1, author = "R. D. C. Monteiro", title = "On the continuous trajectories for a potential reduction algorithm for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Monteiro2, author = "R. D. C. Monteiro and I. Adler", title = "An ${O(n^{3}L)}$ primal--dual interior point algorithm for linear programming", type = "{Technical Report}", number = "ORC~87--4", year = "1987", institution = "Dept.\ of Industrial Engineering and Operations Research, University of California", address = "Berkeley, CA~94720, USA", } @Article{int:Monteiro3, author = "R. D. C. Monteiro and I. Adler", title = "Interior path following primal--dual algorithms~: {Part~I~: L}inear programming", journal = "Mathematical Programming", volume = "44", year = "1989", pages = "27--41", } @Article{int:Monteiro4, author = "R. D. C. Monteiro and I. Adler", title = "Interior path following primal--dual algorithms~: {Part~II~: C}onvex quadratic programming", journal = "Mathematical Programming", volume = "44", year = "1989", pages = "43--66", } @Article{int:Monteiro5, author = "R. D. C. Monteiro and I. Adler", title = "An extension of {Karmarkar}--type algorithm to a class of convex separable programming problems with global linear rate of convergence", journal = "Mathematics of Operations Research", volume = "15", year = "1990", pages = "408--422", } @TechReport{int:Monteiro6, author = "R. D. C. Monteiro and I. Adler", title = "A polynomial primal--dual affine algorithm for {LP}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO, USA}", year = "1988", month = oct, institution = "Engineering Systems Research Center, University of California", address = "Berkeley, CA~94720, USA", } @Article{int:Monteiro7, author = "R. D. C. Monteiro and I. Adler and M. G. C. Resende", title = "A polynomial--time primal--dual affine scaling algorithm for linear and convex quadratic programming and its power series extension", journal = "Mathematics of Operations Research", volume = "15", year = "1990", pages = "191--214", } @TechReport{int:Monteiro8, author = "R. D. C. Monteiro", title = "An implementation of range analysis for {LP} problems solved via interior point methods", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Dept.\ of Systems and Industrial Engineering, University of Arizona", address = "Tucson, AZ~85721, USA", } @InCollection{int:Monteiro9, author = "R. D. C. Monteiro", title = "Convergence and boundary behavior of the projective scaling trajectories for linear programming", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "213--229", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Morin1, author = "T. L. Morin and B. Haas and T. B. Trafalis", title = "Implementation of an interior point algorithm for multiobjective optimization", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ of Mathematics and Computer Science, School of Industrial Engineering, Purdue University", address = "West Lafayette, IN~47907, USA", } @TechReport{int:Morin2, author = "T. L. Morin and T. B. Trafalis", title = "A polynomial--time algorithm for finding an efficient face of a polyhedron", type = "{Technical Report}", year = "1989", month = "", institution = "Dept.\ of Mathematics and Computer Science, School of Industrial Engineering, Purdue University", address = "West Lafayette, IN~47907, USA", } @TechReport{int:Morshedi1, author = "A. M. Morshedi and R. A. Tapia", title = "Karmarkar as a classical method", type = "{Technical Report}", number = "TR~87--7", year = "1987", month = aug, institution = "Rice University, Dept.\ of Mathematical Sciences", address = "Houston, TX~77251, USA", } @TechReport{int:Mueller1, author = "H. M{\"u}ller--Merbach", title = "Right through the interior with the simplex technique", type = "{Technical Report}", year = "1987", institution = "University of Kaiserslautern", address = "D-6100~Kaiserslautern, Germany", bibdate = "Sat Dec 30 09:54:28 1995", } @TechReport{int:Mulvey1, author = "J. M. Mulvey and A. Ruszczynski", title = "A diagonal quadratic approximation method for large scale linear programs", type = "{Technical Report}", number = "SOR~90--08", year = "1990", institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Mulvey2, author = "J. M. Mulvey and A. Ruszczynski", title = "A parallel interior point method for multistage stochastic optimization", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "School of Engineering and Applied Science, Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @InCollection{int:Murray1, author = "W. Murray", title = "Methods for large--scale linear programming", booktitle = "Algorithms and Model Formulations in Mathematical Programming", editor = "S. W. Wallace", series = "NATO ASI Series", volume = "F51", year = "1989", pages = "115--137", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:28 1995", } @TechReport{int:Murray2, author = "S. Murray", title = "An interior point conjugate gradient approach to the generalized flow problem with costs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Murray3, author = "W. Murray and M. H. Wright", title = "Line search procedures for the logarithmic barrier function", type = "Manuscript", year = "1991", institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Murty1, author = "K. G. Murty and Y. Fathi", title = "A feasible direction method for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Boston, MA, USA}", year = "1985", month = apr, institution = "Dept.\ of Operations Research, University of Michigan", address = "Ann Arbor, MI~48103, USA", } @TechReport{int:Murty2, author = "K. G. Murty", title = "A new interior variant of the gradient projection method for linear programming", type = "{Technical Report}", number = "85--18", year = "1985", institution = "Dept.\ of Operations Research, University of Michigan", address = "Ann Arbor, MI~48103, USA", } @Article{int:Murty3, author = "K. G. Murty", title = "The gravitational method for linear programming", journal = "Journal of the Operational Research Society of India (Opsearch)", volume = "23", year = "1986", pages = "206--214", } @InBook{int:Murty4, author = "K. G. Murty", title = "Linear complementarity, linear and nonlinear programming", chapter = "11.4.1~: {The Karmarkar's algorithm for linear programming}", pages = "469--494", series = "Sigma Series in Applied Mathematics", volume = "3", publisher = "Heldermann Verlag", address = "Nassauische~Str.~26, D-1000~Berlin~31, Germany", year = "1988", bibdate = "Sat Dec 30 09:54:28 1995", } @InBook{int:Murty5, author = "K. G. Murty", title = "Linear complementarity, linear and nonlinear programming", chapter = "11.4.4~: {The gravitational method for linear programming}", pages = "498--506", series = "Sigma Series in Applied Mathematics", volume = "3", publisher = "Heldermann Verlag", address = "Nassauische~Str.~26, D-1000~Berlin~31, Germany", year = "1988", bibdate = "Sat Dec 30 09:54:28 1995", } @Article{int:Nash1, author = "S. G. Nash", title = "Optimization at {ICIAM~'91}", journal = "SIAM News", volume = "24", number = "5", year = "1991", month = sep, pages = "16", } @TechReport{int:Nazareth1, author = "J. L. Nazareth", title = "Karmarkar's method and homotopies with restart", type = "{CDSS Report}", year = "1985", institution = "University of California", address = "Berkeley, CA~94720, USA", } @Article{int:Nazareth2, author = "J. L. Nazareth", title = "Homotopy techniques in linear programming", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "529--535", } @InCollection{int:Nazareth3, author = "J. L. Nazareth", title = "Pricing criteria in linear programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", editor = "N. Megiddo", year = "1989", pages = "105--130", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:30 1995", } @TechReport{int:Nazareth4, author = "J. L. Nazareth", title = "Some parallels in the historical development of the simplex and interior point methods for linear programming", type = "{Mathematics Note}", year = "19..(?)", institution = "Dept.\ of Pure and Applied Mathematics, Washington State University", address = "Pullman, WA~99164-2930, USA", } @Article{int:Nazareth5, author = "J. L. Nazareth", title = "The homotopy principle and algorithms for linear programming", journal = "SIAM Journal on Optimization", volume = "1", number = "3", year = "1991", pages = "316--332", } @InBook{int:Nemhauser1, author = "G. L. Nemhauser and L. A. Wolsey", title = "Integer and Combinatorial Optimization", chapter = "I.6.4~: {A} projective algorithm for linear programming", pages = "164--172", publisher = "John Wiley \& Sons", address = "New York, NY, USA", year = "1988", } @Article{int:Nemirovskiy1, author = "A. S. Nemirovskiy", title = "An algorithm of the {Karmarkar} type", journal = "Teknicheskaya Kibernetika", volume = "1", year = "1987", pages = "105--118", note = "Translated in~: {\em Soviet Journal on Computers and System Sciences}, 25(5):61--74, 1987", } @Article{int:Nemirovskiy2, author = "A. S. Nemirovskiy", title = "An new polynomial algorithm for linear programming", journal = "Doklady Akademii Nauk SSSR", volume = "298", number = "6", year = "1988", pages = "1321--1325", note = "Translated in~: {\em Soviet Mathematics Doklady}, 37(1): 264--269, 1988", } @Article{int:Nesterov1, author = "Y. Y. Nesterov", title = "Polynomial methods in the linear and quadratic programming", journal = "Teknicheskaya Kibernetika", volume = "3", year = "1988", pages = "3--6", note = "Translated in~: {\em Soviet Journal on Computers and System Sciences}, 26:98--101, 1988", } @Article{int:Nesterov2, author = "Y. Y. Nesterov", title = "Polynomial--time dual algorithms for linear programming", journal = "Kibernetika", volume = "25", number = "1", year = "1989", pages = "34--40", note = "Translated in~: {\em Cybernetics}, 25(1):40--49, 1989", } @Article{int:Nesterov3, author = "Y. Y. Nesterov and A. S. Nemirovsky", title = "Acceleration and parallelization of the path--following interior point method for a linearly constrained convex quadratic problem", journal = "SIAM Journal on Optimization", volume = "1", number = "4", year = "1991", pages = "548--564", } @TechReport{int:Neumann1, author = "{J. von} Neumann", title = "On a maximization problem", type = "Manuscript", year = "1947", institution = "Institute for Advanced Studies, Princeton University", address = "Princeton, NJ 08544, USA", } @Article{int:Nickel1, author = "W. Nickel and W. R{\"o}dder and L. Xu and H. J. Zimmermann", title = "Intelligent gradient search in linear programming", journal = "European Journal of Operational Research", volume = "22", year = "1985", pages = "293--303", } @TechReport{int:Noma1, author = "T. Noma and N. Megiddo and M. Kojima and A. Yoshise", title = "Some classes of linear complementarity problems that can be processed by interior point methods", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Dept.\ of Information Science, Tokyo Institute of Technology", address = "2-12-1~Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @TechReport{int:Noma2, author = "T. Noma and M. Kojima", title = "A global, convergent iterative algorithm for complementarity problems", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Dept.\ of Information Science, Tokyo Institute of Technology", address = "2-12-1~Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @PhdThesis{int:Noma3, author = "T. Noma", title = "A globally convergent iterative algorithm for complementarity problems~: {A} modification of interior point algorithms for linear complementarity problems", year = "1991", school = "Dept.\ of Information Science, Tokyo Institute of Technology", address = "2-12-1~Oh-Okayama, Meguro-ku, Tokyo~152, Japan", } @PhdThesis{int:Nunez1, author = "M. A. {Nunez Araya}", title = "Experiments using variants of {Dikin's} ellipsoid method for solving mathematical programs", year = "1990", school = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Nurminskii1, author = "E. A. Nurminskii and S. K. Andrusenko and P. I. Stetsyuk", title = "A new polynomial algorithm for linear programming", journal = "Kibernetika (Kiev)", volume = "4", year = "1985", pages = "118--120, 136", note = "(In Russian, English summary)", } @InCollection{int:Oohori1, author = "T. Oohori and A. Ohuchi", title = "Symbolic generation of an optimal {Karmarkar}'s algorithm for sparse linear programs", booktitle = "System Modelling and Optimization~: Proceedings of the 14th IFIP--Confernce, Leipzig, East Germany, July 1989", editor = "H. J. Sebastian and K. Tammer", year = "1990", pages = "194--203", series = "Lecture Notes in Control and Information Science", volume = "143", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:54 1995", } @Article{int:Osborne1, author = "M. R. Osborne", title = "Dual barrier functions with superfast rates of convergence for the linear programming problem", journal = "Journal of the Australian Mathematical Society, Ser.~B", volume = "29", year = "1987", pages = "39--58", } @Article{int:Osborne2, author = "M. R. Osborne", title = "An interior point method for linear programming", journal = "Journal of the Australian Mathematical Society, Ser.~B", volume = "31", year = "1990", pages = "367--378", } @TechReport{int:Padberg1, author = "M. W. Padberg", title = "Solution of a nonlinear programming problem arising in the projective method for linear programming", type = "{Technical Report}", year = "1985", month = mar, institution = "School of Business and Administration, New York University", address = "New York, NY~10003, USA", note = "To appear in {\em SIAM Journal on Control and Optimization}", } @Article{int:Padberg2, author = "M. W. Padberg", title = "A different convergence proof of the projective method for linear programming", journal = "Operations Research Letters", volume = "4", year = "1986", pages = "253--257", } @TechReport{int:Pai1, author = "R. Pai and N. K. Karmarkar and {S. S.} S. P. Rao", title = "A global router based on {Karmarkar}'s interior point method", type = "{CSE Technical Report}", year = "1988", month = apr, institution = "Indian Institute of Technology", address = "Bombay, India", } @Article{int:Pan1, author = "V. Pan", title = "The modified barrier function method for linear programming and its extension", journal = "Computers and Mathematics with Applications", volume = "20", number = "3", year = "1990", pages = "1--14", } @Article{int:Pan2, author = "V. Pan and J. Reif", title = "Efficient parallel linear programming", journal = "Operations Research Letters", volume = "5", year = "1986", pages = "127--135", } @Article{int:Pan3, author = "V. Pan and J. Reif", title = "Fast and efficient linear programming and linear least--squares computations", journal = "Computers and Mathematics with Applications Ser.~A", volume = "12", year = "1986", pages = "1217--1227", } @TechReport{int:Pardalos1, author = "P. M. Pardalos", title = "Interior point algorithms for nonconvex quadratic problems", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Dept.\ of Computer Science, Pennsylvania State University", address = "University Park, PA~16802, USA", } @TechReport{int:Pardalos2, author = "P. M. Pardalos and C. G. Han and Y. Ye", title = "Computational aspects of an interior point algorithm for quadratic problems with box constraints", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Dept.\ of Computer Science, Pennsylvania State University", address = "University Park, PA~16802, USA", } @TechReport{int:Pardalos3, author = "P. M. Pardalos and Y. Ye and C. G. Han", title = "Parallel computing in quadratic programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ Computer Science, Pennsylvania State University", address = "University Park, PA~16802, USA", } @Article{int:Pardalos4, author = "P. M. Pardalos and Y. Ye and C. G. Han", title = "Algorithms for the solution of quadratic knapsack problems", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "69--91", } @InCollection{int:Pardalos5, author = "P. M. Pardalos and Y. Ye and C. G. Han", title = "An interior point algorithm for large--scale quadratic problems with box constraints", booktitle = "Analysis and Optimization of Systems~: Proceedings of the 9th International Conference, Antibes, France, 1990", editor = "A. Bensoussan and J. L. Lions", year = "1990", pages = "413--422", series = "Lecture Notes in Control and Information Science", volume = "144", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:30 1995", } @Article{int:Pardalos6, author = "P. M. Pardalos", title = "Polynomial time algorithms for some classes of constrained nonconvex quadratic problems", journal = "Optimization", volume = "21", year = "1990", pages = "843--853", } @TechReport{int:Pardalos7, author = "P. M. Pardalos and C. G. Han and J. A. Kaliski and Y. Ye", title = "Solution of quadratic programming and linear complementarity problems using a potential reduction algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Computer Science, Pennsylvania State University", address = "University Park, PA~16802, USA", } @TechReport{int:Pardalos8, author = "P. M. Pardalos and Y. Ye and C. G. Han and J. A. Kaliski", title = "Solution of {$P_{0}$}--matrix linear complementarity problems using a potential reduction algorithm", type = "{Technical Report}", number = "CS--90--32", year = "1990", institution = "Dept.\ of Computer Science, Pennsylvania State University", address = "University Park, PA~16802, USA", note = "To appear in {\em SIAM Journal on Matrix Analysis and Applications, 1991}", } @Article{int:Pardalos9, author = "P. M. Pardalos and C. G. Han and Y. Ye", title = "Interior--point algorithms for solving nonlinear optimization problems", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "45--54", } @Article{int:Paris1, author = "Q. Paris", title = "A primer on {Karmarkar}'s algorithm for linear programming", journal = "METU Studies in Develpoment", volume = "12", number = "1--2", year = "1985", pages = "131--155", } @Article{int:Parisot1, author = "G. R. Parisot", title = "Resolution numerique approchee du probleme de programmation lineaire par application de la programmation logarithmique {(Approximate numerical solution of linear programming problems by an application of the logarithmic programming)}", journal = "Revue Francaise Recherche Operationelle", volume = "20", year = "1961", pages = "227--259", note = "(In French)", } @InBook{int:Parker1, author = "R. G. Parker and R. L. Rardin", title = "Discrete Optimization", chapter = "4.1.3~: {Karmarkar}'s projection scaling algorithm", year = "1988", pages = "117--131", publisher = "Academic Press", address = "New York, NY, USA", } @Article{int:Philpott1, author = "A. B. Philpott", title = "Linear programming made simpler than simplex", journal = "New Scientist", year = "1984", month = "December 6,", pages = "20", } @TechReport{int:Pickel1, author = "P. F. Pickel", title = "Approximate projections for the {Karmarkar} algorithm", type = "Manuscript", year = "1985", institution = "Polytechnic Institute of New York", address = "Farmingdale, NY, USA", } @TechReport{int:Pickel2, author = "P. F. Pickel", title = "Implementing the {Karmarkar} algorithm using simplex techniques", type = "{Talk held at the 12th International Symposium on Mathematical Programming in Cambridge, MA, USA}", year = "1985", institution = "Polytechnic Institute of New York", address = "Farmingdale, NY, USA", } @TechReport{int:Pickel3, author = "P. F. Pickel", title = "Preliminary computational experience with approximate projections in the {Karmarkar} algorithm", type = "{Technical Report}", year = "1986", institution = "Polytechnic Institute of New York", address = "Farmingdale, NY, USA", } @TechReport{int:Polyak1, author = "R. Polyak", title = "Modified interior distance function in linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Mathematical Sciences Department, IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @TechReport{int:Polyak2, author = "R. Polyak", title = "Interior point methods, nonlinear and parallel optimization", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Mathematical Sciences Department, IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @TechReport{int:Polyak3, author = "R. Polyak", title = "Modified barrier function~: {Theory} and practice", type = "{Technical Report}", number = "RC~15886", year = "1990", institution = "Mathematical Sciences Department, IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @TechReport{int:Polyak4, author = "R. Polyak", title = "Modified barrier functions in linear programming", type = "{Collected Abstracts}", year = "1988", institution = "Mathematical Sciences Department, IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @TechReport{int:Polyak5, author = "R. Polyak", title = "The nonlinear rescaling principle in linear programming", type = "{Technical Report}", number = "RC~15030~(67093)", year = "1989", institution = "Mathematical Sciences Department, IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @Article{int:Polyak6, author = "R. Polyak", title = "Modified barrier and center methods", journal = "Reports from the Moscow Refusnik Seminar, Annals of the New York Academy of Sciences", volume = "491", year = "1987", pages = "194--196", } @PhdThesis{int:Ponceleon1, author = "D. B. Ponceleon", title = "Barrier methods for large--scale quadratic programming", year = "1990", school = "Computer Science Department, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ponceleon2, author = "D. B. Ponceleon", title = "Barrier methods for large--scale quadratic programming", type = "{Technical Report}", number = "SOL~91--2", year = "1991", month = jun, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ponnambalam1, author = "K. Ponnambalam", title = "Large scale nonlinear programming using interior point and successive linear programming methods", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Faculty of Engineering, Dept.\ of Electrical Engineering, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", } @TechReport{int:Ponnambalam2, author = "K. Ponnambalam and A. Vannelli", title = "New starting and stopping steps for the dual affine variant of {Karmarkar}'s method", type = "{Technical Report}", year = "1988", institution = "Faculty of Engineering, Dept.\ of Electrical Engineering, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", } @TechReport{int:Ponnambalam3, author = "K. Ponnambalam and A. Vannelli", title = "An inexpensive basis recovery procedure for {Karmarkar}'s dual affine method", type = "{Technical Report}", year = "1989", institution = "Faculty of Engineering, Dept.\ of Electrical Engineering, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", } @TechReport{int:Ponnambalam4, author = "K. Ponnambalam and A. Vannelli and T. E. Unny", title = "An application of {Karmarkar}'s interior point linear programming algorithm for multi--reservoir operations optimization", type = "{Technical Report}", year = "1988", institution = "Faculty of Engineering, Dept.\ of Electrical Engineering, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", note = "To appear in {\em Stochastic Hydrology and Hydraulics}", } @TechReport{int:Ponnambalam5, author = "K. Ponnambalam", title = "An interior point algorithm for large scale nonlinear programming", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "Faculty of Engineering, Dept.\ of Electrical Engineering, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", } @InCollection{int:Ponnambalam6, author = "K. Ponnambalam and S. Seetharaman and T. Alguindigue", title = "Affine algorithms for {$L$}--minimization", booktitle = "Proceedings of the Sixth Multidimensional Signal Processing Workshop held in Pacific Grove, CA, USA, September 1989", year = "1989", pages = "115", publisher = "IEEE", address = "New York, NY, USA", } @TechReport{int:Poore1, author = "A. B. Poore and D. Soria", title = "Continuation algorithms for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New Orleans, USA}", year = "1987", month = may, institution = "Dept.\ of Mathematics, Colorado State University", address = "Fort Collins, CO~80253, USA", } @TechReport{int:Potra1, author = "F. A. Potra and Y. Ye", title = "Interior point methods for nonlinear complementarity problems", type = "{Working Paper}", year = "1991", institution = "Dept.\ of Management Sciences, The University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Potra2, author = "F. A. Potra", title = "Implementation of interior point methods on parallel machines", type = "{Talk held at the 16. Symposium on Operations Research in Trier, Germany}", year = "1991", month = sep, institution = "Dept.\ of Management Sciences, The University of Iowa", address = "Iowa City, IA~52242, USA", bibdate = "Sat Dec 30 09:54:30 1995", } @TechReport{int:Powell1, author = "M. J. D. Powell", title = "Is {Karmarkar}'s method suitable for semi--infinite programming~?", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "University of Cambridge", address = "Cambridge, UK", } @Article{int:Powell2, author = "M. J. D. Powell", title = "Karmarkar's algorithm~: {A} view from nonlinear programming", journal = "Bulletin of the Institute of Mathematics and Its Applications", volume = "26", number = "8--9", year = "1990", pages = "165--181", } @InCollection{int:Radosavljevic1, author = "M. D. Radosavljevic--Nicolic", title = "Asymptotic behavior of the affine scaling variant of {Karmarkar}'s algorithm for linear programming", booktitle = "Proceedings of the XX--th Conference `Mathematical Optimization', Humboldt Universit{\"a}t Berlin, East Germany", year = "1990", bibdate = "Sat Dec 30 09:54:56 1995", } @Article{int:Rajasekera1, author = "J. R. Rajasekera and S. C. Fang", title = "On the convex programming approach to linear programming", journal = "Operations Research Letters", volume = "10", year = "1991", pages = "309--312", } @Article{int:Renegar1, author = "J. Renegar", title = "A polynomial--time algorithm, based on {Newton}'s method, for linear programming", journal = "Mathematical Programming", volume = "40", year = "1988", pages = "59--93", } @TechReport{int:Renegar2, author = "J. Renegar", title = "Path--following methods in linear programming", type = "{Technical Report}", year = "1988", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Renegar3, author = "J. Renegar and M. Shub", title = "Simplified complexity analysis for {Newton LP} methods", type = "{Technical Report}", number = "807", year = "1988", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Resende1, author = "M. G. C. Resende", title = "A generalized quadratic form potential for an interior point algorithm for integer programming", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Mathematical Sciences Research Center, AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Resende2, author = "M. G. C. Resende and G. Veiga", title = "An implementation of the dual affine scaling algorithm for network flow problems", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Resende3, author = "M. G. C. Resende and M. H. Wright", title = "Sixty--six attend interior methods workshop at {Asilomar}", journal = "SIAM News", volume = "23", number = "3", year = "1990", month = may, pages = "9", } @TechReport{int:Resende4, author = "M. G. C. Resende and G. Veiga", title = "A dual affine scaling algorithm for network flows", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Resende5, author = "M. G. C. Resende and N. K. Karmarkar and A. P. Kamath and K. G. Ramakrishnan", title = "An interior point approach to graph partitioning", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Resende6, author = "M. G. C. Resende and G. Veiga and I. Adler", title = "Experimentation with interior point implementations", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Resende7, author = "M. G. C. Resende and G. Veiga", title = "A dual affine scaling algorithm for minimum cost network flow problems", type = "{Technical Report}", number = "1.3", year = "1990", month = nov, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", note = "Revised February 1991", } @TechReport{int:Resende8, author = "M. G. C. Resende and G. Veiga", title = "Computational investigation of an interior point linear programming algorithm for minimum cost network flow", type = "{Technical Report}", number = "1.0", year = "1991", month = aug, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Resende9, author = "M. G. C. Resende and A. P. Kamath and N. K. Karmarkar and K. G. Ramakrishnan", title = "Mathematical programming approach to inductive inference", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Mathematical Sciences Research Center, AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @InBook{int:Richter1, author = "C. Richter", title = "{Optimierungsverfahren und BASIC--Programme (Optimization Methods and BASIC--Programs)}", chapter = "2.3.2~: {Das Projektionsverfahren von Karmarkar (The projection method of Karmarkar), pages 47--50, P.2.4.~: Projektionsverfahren, BASIC--Programm}", year = "1988", pages = "123--124", publisher = "Akademie Verlag", address = "D-1000 Berlin, Germany", note = "(In German)", } @Article{int:Rinaldi1, author = "G. Rinaldi", title = "A projective method for linear programming with box--type constraints", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "517--527", } @Article{int:Rockett1, author = "A. M. Rockett and J. C. Stevenson", title = "{Karmarkar}'s algorithm~: {A} method for solving large linear programming", journal = "BYTE", volume = "12", number = "10", year = "1987", pages = "146--162", } @Article{int:Roehrkasse1, author = "R. Roehrkasse", title = "Linear programming and {Operations Research}", journal = "IEEE Potentials", volume = "9", number = "4", year = "1990", month = dec, pages = "39--40", } @TechReport{int:Roos1, author = "C. Roos", title = "On {Karmarkar}'s projective method for linear programming", type = "{Technical Report}", number = "85--23", year = "1985", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos2, author = "C. Roos", title = "Linear programming along the trajectory of the problem", type = "{Technical Report}", number = "87--41", year = "1987", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos3, author = "C. Roos", title = "On the trajectory of a linear programming problem", type = "{Technical Report}", number = "87--53", year = "1987", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos4, author = "C. Roos", title = "A new trajectory--following polynomial--time algorithm for the linear programming problem", type = "{Technical Report}", number = "87--87", year = "1987", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos5, author = "C. Roos", title = "Linear programming along the trajectory of the problem in polynomial time", type = "{Technical Report}", number = "88--17", year = "1988", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos6, author = "C. Roos", title = "The influence of the potential function on the performance of a trajectory following algorithm for the linear programming problem", type = "{Technical Report}", number = "88--44", year = "1988", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @Article{int:Roos7, author = "C. Roos", title = "New trajectory--following polynomial--time algorithm for linear programming problems", journal = "Journal of Optimization Theory and Applications", volume = "63", year = "1989", pages = "433--458", } @InCollection{int:Roos8, author = "C. Roos", title = "An ${O(n^{3}L)}$ approximate center method for linear programming", booktitle = "Optimization~: Proceedings of the 5th French--German Conference in Castel--Novel, Varetz, France, October 1988", editor = "S. Dolecki", year = "1989", pages = "147--158", series = "Lecture Notes in Mathematics", volume = "1405", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:32 1995", } @TechReport{int:Roos9, author = "C. Roos", title = "Polynomial--time algorithms for linear programming based on the use of the logarithmic barrier penalty function", type = "{Talk held at the 14th Conference on the Mathematics of Operations Research in Dalfsen, The Netherlands}", year = "1990", month = jan, institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos10, author = "C. Roos", title = "A potential reduction method for a class of a smooth convex programming problem", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos11, author = "C. Roos and {D. den} Hertog", title = "A polynomial method of approximate weighted centers for linear programming", type = "{Technical Report}", number = "89--13", year = "1989", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos12, author = "C. Roos and J. P. Vial", title = "A polynomial method of approximate centers for linear programming", type = "{Technical Report}", number = "88--68", year = "1988", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", note = "Submitted to {\em Mathematical Programing}", } @TechReport{int:Roos13, author = "C. Roos and J. P. Vial", title = "Analytic centers in linear programming", type = "{Technical Report}", number = "88--74", year = "1988", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @InCollection{int:Roos14, author = "C. Roos and J. P. Vial", title = "Long steps with the logarithmic penalty barrier function in linear programming", booktitle = "Economic Decision--Making~: Games, Economics and Optimization, dedicated to J. H. Dreze", editor = "J. Gabszevwicz and J. F. Richard and L. Wolsey", year = "1989", pages = "433--441", publisher = "Elsevier Science Publisher B.V.", address = "Amsterdam, The Netherlands", } @TechReport{int:Roos15, author = "C. Roos", title = "A pivoting rule of the simplex method which is related to {Karmarkar}'s potential function", type = "{Technical Report}", year = "1985", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @TechReport{int:Roos16, author = "C. Roos", title = "A projective variant of the approximate center method for linear programming", type = "{Technical Report}", number = "90--83", year = "1990", institution = "Faculty of Mathematics and Informatics, TU Delft", address = "NL-2628~BL~Delft, The Netherlands", } @Book{int:Roos17, author = "C. Roos and J. P. Vial", title = "Interior Point Methods, Theory and Practice~: Proceedings of the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, held in Scheveningen, The Netherlands, January 1990", year = "1991", series = "Mathematical Programming, Series~B", publisher = "North Holland", address = "Amsterdam, The Netherlands", } @Article{int:Ruzinsky1, author = "S. A. Ruzinsky and E. T. Olsen", title = "${L_1}$ and ${L_\infty}$ minimization via a variant of {Karmarkar}'s algorithm", journal = "IEEE Transactions on Acoustics, Speech, and Signal Processing", volume = "37", number = "2", year = "1989", pages = "245--253", } @TechReport{int:Saigal1, author = "R. Saigal", title = "Tracing homotopy paths in polynomial time", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Dept.\ of Industrial and Operational Engineering, University of Michigan", address = "Ann Arbor, MI~48109-2117, USA", } @TechReport{int:Saigal2, author = "R. Saigal", title = "Interior point methods for the transportation problem", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "Dept.\ of Industrial and Operational Engineering, University of Michigan", address = "Ann Arbor, MI~48109-2117, USA", } @TechReport{int:Saigal3, author = "R. Saigal", title = "{SOR}--type iterative techniques for interior point methods", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Dept.\ of Industrial and Operational Engineering, University of Michigan", address = "Ann Arbor, MI~48109-2117, USA", } @TechReport{int:Salamanca1, author = "A. Salamanca", title = "An inner ellipsoid algorithm for linear programming", type = "{Technical Report}", number = "1--ABR/86", year = "1986", institution = "Dept.\ of Mathematics, E.~T.~S. de Ingenieros Industriales, Universidad Politecmia de Madrid", address = "Madrid, Spain", } @Article{int:Salhi1, author = "A. Salhi and G. R. Lindfield", title = "Effects of ordering and updating techniques on the performance of the {Karmarkar} algorithm", journal = "R.A.I.R.O. Recherche Operationnelle/Operations Research", volume = "25", number = "2", year = "1991", pages = "209--236", } @TechReport{int:Saltzman1, author = "M. J. Saltzman", title = "Parallel implementation of interior point {LP} algorithms", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Dept.\ of Mathematical Sciences, Clemson University", address = "Clemson, SC~29634-1907, USA", } @InCollection{int:Saltzman2, author = "M. J. Saltzman and R. Subramaniam and R. E. Marsten", title = "Implementing an interior point {LP} algorithm on a supercomputer", booktitle = "Impacts of Recent Computer Advances on Operations Research", publisher = "North Holland", address = "Amsterdam, The Netherlands", editor = "R. Sharda and B. L. Golden and E. Wasil and O. Balci and W. Stewart", year = "1989", pages = "158--168", } @TechReport{int:Saltzman3, author = "M. J. Saltzman", title = "{WRIP~: A workbench for research in interior point methods}", type = "{Panel--Discussion held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Dept.\ of Mathematical Sciences, Clemson University", address = "Clemson, SC~29634-1907, USA", } @TechReport{int:Samuelsen1, author = "C. M. Samuelsen and R. A. Tapia", title = "The {Dikin--Karmarkar} principle for steepest descent", type = "{Talk held at the Second International Conference on Industrial and Applied Mathematics (ICIAM~'91), Washington, DC, USA}", year = "1991", month = jul, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Schneider1, author = "W. Schneider", title = "An inner point preprocessing procedure", type = "{Talk held at the DGOR--Jahrestagung in Stuttgart--Hohernheim, Germany}", year = "1991", month = sep, institution = "Institut f{\"u}r Informatik, Universit{\"a}t Linz", address = "P.~O.~Box, A-4040~Linz, Austria", bibdate = "Sat Dec 30 09:54:32 1995", } @Article{int:Schoenlein1, author = "A. Sch{\"o}nlein", title = "{Der Algorithmus von Karmarkar---Idee, Realisation, Beispiel und numerische Erfahrungen (The Karmarkar algorithm---idea, realisation, example and numerical experiences)}", journal = "Angewandte Informatik", volume = "8", year = "1986", pages = "344--353", note = "(In German)", } @InCollection{int:Schreck1, author = "H. Schreck", title = "Experiences with an implementation of {Karmarkar}'s {LP}--algorithm", booktitle = "Proceedings of the X.~Symposium on Operations Research, Munich, Germany, August 1985", editor = "M. J. Beckmann and K. W. Gaede and K. Ritter and H. Schneeweiss", series = "Methods of Operations Research", volume = "54", year = "1986", pages = "535--542", publisher = "Anton Hain Meisenheim Verlag", address = "K{\"o}nigstein-Taunus, West-Germany", bibdate = "Sat Dec 30 09:54:32 1995", } @Article{int:Schrijver1, author = "A. Schrijver", title = "The new linear programming method of {Karmarkar}", journal = "CWI Newsletter", volume = "8", year = "1985", pages = "2--14", } @InBook{int:Schrijver2, author = "A. Schrijver", title = "Theory of Linear and Integer Programming", chapter = "15.1~: {Karmarkar}'s polynomial--time algorithm for linear programming", pages = "190--194", publisher = "John Wiley \& Sons", address = "New York, NY, USA", year = "1986", } @TechReport{int:Schrijver3, author = "A. Schrijver", title = "The algorithm of {N.~K.~Karmarkar} for linear programming", type = "{Talk held at the 14th Conference on the Mathematics of Operations Research in Dalfsen, The Netherlands}", year = "1990", month = jan, institution = "Centre for Mathematics and Computer Science (CWI)", address = "Kruislaan 413, NL-1098~SJ~Amsterdam, The Netherlands", } @TechReport{int:Schultz1, author = "G. L. Schultz and R. R. Meyer", title = "A structured interior point method", type = "{Technical Report}", number = "934", year = "1990", institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @Article{int:Schultz2, author = "H. Schultz and W. Pulleyblank", title = "Trends in optimization", journal = "OR/MS Today", volume = "18", number = "4", year = "1991", month = aug, pages = "20--25", } @Article{int:Schultz3, author = "G. L. Schultz and R. R. Meyer", title = "An interior point method for block angular optimization", journal = "SIAM Journal on Optimization", volume = "1", number = "4", year = "1991", pages = "583--602", } @TechReport{int:Setiono1, author = "R. Setiono", title = "An interior dual proximal--point algorithm for linear programs", type = "{Technical Report}", number = "879", year = "1989", institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @TechReport{int:Setiono2, author = "R. Setiono", title = "Interior proximal--point algorithm for linear programs", type = "{Technical Report}", number = "949", year = "1990", institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @TechReport{int:Setiono3, author = "R. Setiono", title = "Interior dual least 2--norm algorithm for linear programs", type = "{Technical Report}", number = "950", year = "1990", institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @TechReport{int:Setiono4, author = "R. Setiono", title = "Interior dual proximal--point algorithm using preconditioned conjugate gradient", type = "{Technical Report}", number = "951", year = "1990", institution = "Dept.\ of Computer Science, University of Wisconsin", address = "Madison, WI~53706, USA", } @Article{int:Shanno1, author = "D. F. Shanno", title = "Computing {Karmarkar} projections quickly", journal = "Mathematical Programming", volume = "41", year = "1988", pages = "61--71", } @TechReport{int:Shanno2, author = "D. F. Shanno", title = "Interior--point methods for linear programming~: {The} state--of--the--computational--art", type = "{Talk held at the Symposium on Mathematical Programming in Oberwolfach, Germany}", year = "1990", month = jan, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", bibdate = "Sat Dec 30 09:54:32 1995", } @TechReport{int:Shanno3, author = "D. F. Shanno", title = "Interior--point methods for linear programming~: {The} state--of--the--art", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @Article{int:Shanno4, author = "D. F. Shanno and A. Bagchi", title = "A unified view of interior point methods for linear programming", journal = "Annals of Operations Research", volume = "22", year = "1990", pages = "55--70", } @TechReport{int:Shanno5, author = "D. F. Shanno and R. E. Marsten", title = "On implementing {Karmarkar}'s method", type = "{Working Paper}", number = "85--01", year = "1985", institution = "Graduate School of Administration, University of California", address = "Davis, CA~95616, USA", } @TechReport{int:Shanno6, author = "D. F. Shanno and R. E. Marsten", title = "Implementation of the {Karmarkar} algorithm within {XMP} framework", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach, FL, USA}", year = "1986", month = oct, institution = "Graduate School of Administration, University of California", address = "Davis, CA~95616, USA", } @Article{int:Shanno7, author = "D. F. Shanno and R. E. Marsten", title = "A reduced--gradient variant of {Karmarkar}'s algorithm and null--space projections", journal = "Journal of Optimization Theory and Applications", volume = "57", year = "1988", pages = "383--397", } @TechReport{int:Shanno8, author = "D. F. Shanno and R. E. Marsten", title = "Interior point methods for linear programming~: {Ready} for production use", type = "{Workshop held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Shanno9, author = "D. F. Shanno and R. E. Marsten", title = "Set partitioning via interior point methods", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Shanno10, author = "D. F. Shanno and C. L. Monma and K. McShane", title = "Computational experience with a primal--dual method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Shanno11, author = "D. F. Shanno and R. E. Marsten and M. J. Saltzman and R. Subramaniam", title = "Solving set partitioning problems with cutting planes and an interior point method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Shanno12, author = "D. F. Shanno", title = "An overview of interior point methods with implementation details and computational experience", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Shanno13, author = "D. F. Shanno and T. J. Carpenter", title = "{\em Log}--barrier methods for quadratic and linearly constrained nonlinear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @TechReport{int:Shanno14, author = "D. F. Shanno", title = "Current state of primal--dual interior code", type = "{Talk held at the Second Asilomar Workshop on Progress in Mathematical Programming, Asimolar Conference Center, Pacific Grove, CA, USA}", year = "1990", month = mar, institution = "RUTCOR Center of Operations Research, Rutgers University", address = "New Brunswick, NJ~08903, USA", } @Article{int:Sherali1, author = "H. D. Sherali", title = "Algorithmic insights and a convergence analysis for a {Karmarkar}--type of algorithm for linear programming problems", journal = "Naval Research Logistics Quarterly", volume = "34", year = "1987", pages = "399--416", } @Article{int:Sherali2, author = "H. D. Sherali and B. O. Skarpness and B. Kim", title = "An assumption--free convergence analysis of the scaling algorithm for linear programs, with application to the ${L_1}$ estimation problem", journal = "Naval Research Logistics Quarterly", volume = "35", year = "1988", pages = "473--492", } @TechReport{int:Sheu1, author = "R. Sheu and S. C. Fang", title = "On the relationship of interior point methods", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Operations Research Program, North Carolina State University", address = "Raleigh, NC~27695, USA", } @Article{int:Shi1, author = "M. G. Shi", title = "Some convergence problems of interior point algorithms for linear programming", journal = "Journal of the Tsinghua University", volume = "28", number = "3", year = "1988", pages = "91--101", note = "(In Chinese)", } @Article{int:Shub1, author = "M. Shub", title = "On the asymptotic behavior of the projective rescaling algorithm for linear programming", journal = "Journal of Complexity", volume = "3", year = "1987", pages = "258--269", } @TechReport{int:Shub2, author = "M. Shub", title = "Boundary and asymptotic behavior of interior point methods for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "IBM~T.~J.~Watson Research Center", address = "Yorktown Heights, NY~10598, USA", } @Article{int:Siam1, key = "Siam", title = "New algorithm stirs interest", journal = "SIAM News", volume = "13", number = "1", year = "1985", month = jan, pages = "1, 17", } @Article{int:Singh1, author = "D. Singh and J. N. Singh", title = "Some remarks on {Karmarkar}'s algorithm for linear programming", journal = "Journal of the Bihar Mathematical Society", volume = "11", year = "1987/88", pages = "85--90", } @InProceedings{int:Sinha1, author = "L. P. Sinha and B. A. Freedman and N. K. Karmarkar and A. Puchta and K. G. Ramakrishnan", title = "Overseas network planning---{Application} of {Karmarkar}'s algorithm", booktitle = "Proceedings of NETWORK~'86 Conference, Tarpon Spring, FL, USA", year = "1986", month = jun, } @TechReport{int:Slutsman1, author = "L. Slutsman", title = "Implementation of primal--dual series algorithm for convex separable quadratic programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "AT~\&~T~Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @InCollection{int:Snyman1, author = "J. A. Snyman and M. van Royen", title = "A multiplex algorithm for linear programming problems", booktitle = "System Modelling and Optimization~ Proceedings of the 13th IFIP Conference, Tokyo, Japan, Aug./Sept.~1987", editor = "M. Iri and K. Yajima", year = "1988", pages = "177--186", series = "Lecture Notes in Control and Information Sciences", volume = "113", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:34 1995", } @Article{int:Snyman2, author = "J. A. Snyman", title = "An interior feasible direction method with constraint projections for linear programming", journal = "Computers and Mathematics with Applications", volume = "20", number = "12", year = "1990", pages = "43--54", } @InCollection{int:Sonnevend1, author = "G. Sonnevend", title = "A new method for solving a set of linear (convex) inequalities and its applications for identification and optimization", booktitle = "Proceedings of the 5th IFAC--IFORS Conference held in Budapest, Hungaria, June 1986", editor = "B. Martos", year = "1987", publisher = "Pergamon Press", address = "Oxford, UK", } @InCollection{int:Sonnevend2, author = "G. Sonnevend", title = "An `analytic center' for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming", booktitle = "System Modelling and Optimization~: Proceedings of the 12th IFIP--Conference held in Budapest, Hungary, September 1985", editor = "A. Prekopa and J. Szelezsan and B. Strazicky", year = "1986", pages = "866--876", series = "Lecture Notes in Control and Information Sciences", volume = "84", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:34 1995", } @InCollection{int:Sonnevend3, author = "G. Sonnevend", title = "New algorithms in convex programming based on a notion of `centre' (for systems of analytic inequalities) and on rational extrapolation", booktitle = "Trends in Mathematical Optimization~: Proceedings of the 4th French--German Conference on Optimization in Irsee, Germany, April 1986", editor = "K. H. Hoffmann and J. B. Hiriat--Urruty and C. Lemarechal and J. Zowe", year = "1988", pages = "311--327", series = "International Series of Numerical Mathematics", volume = "84", publisher = "Birkh{\"a}user Verlag", address = "Basel, Switzerland", bibdate = "Sat Dec 30 09:54:34 1995", } @TechReport{int:Sonnevend4, author = "G. Sonnevend", title = "Application of analytic centers to the design of observers and feedback controllers", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700 W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:54:34 1995", } @Article{int:Sonnevend5, author = "G. Sonnevend and J. Stoer", title = "Global ellipsoid approximations and homotopy methods for solving convex analytic programs", journal = "Applied Mathematics~\&~Optimization", volume = "21", year = "1990", pages = "139--166", } @Article{int:Sonnevend6, author = "G. Sonnevend and J. Stoer and G. Zhao", title = "On the complexity of following the central path by linear extrapolation in linear programming", journal = "Methods of Operations Research", volume = "62", year = "1990", pages = "19--31", } @Article{int:Sonnevend7, author = "G. Sonnevend", title = "Applications of the notion of analytic center in approximation (estimation) problem", journal = "Journal of Computational and Applied Mathematics", volume = "28", year = "1989", pages = "349--358", } @InCollection{int:Sonnevend8, author = "G. Sonnevend", title = "Applications of analytic centers for the numerical solution of semiinfinte, convex programs arising in control theory", booktitle = "System Modelling and Optimization~: Proceedings of the 14th IFIP--Conference, Leipzig, East Germany, July 1989", editor = "H. J. Sebastian and K. Tammer", year = "1990", pages = "413--422", series = "Lecture Notes in Control and Information Sciences", volume = "143", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:58 1995", } @TechReport{int:Sonnevend9, author = "G. Sonnevend and J. Stoer and G. Zhao", title = "On the complexity of following the central path of linear programs by linear extrapolation", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", number = "", year = "1990", month = jan, institution = "Insitut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700 W{\"u}rzburg, Germany", note = "To appear in {\em Mathematical Programming, Series~B, 1991}", bibdate = "Sat Dec 30 09:54:36 1995", } @Article{int:Spiegel1, key = "Spiegel", title = "{Neuer Dampf (New power)}", journal = "Der Spiegel", volume = "38", number = "49", year = "1984", pages = "239--240", note = "(In German)", } @MastersThesis{int:Steger1, author = "A. E. Steger", title = "An extension of {Karmarkar}'s algorithm for bounded linear programming problems", year = "1985", month = aug, school = "Dept.\ of Applied Mathematics, State University of New York", address = "Stony Brook, NY~11794, USA", note = "Condensed version in~: H. Schellhaas, {P. van} Beek, H. Isermann, R. Schmidt and M. Zijlstra, editors, {\em Operations Research Proceedings 1987}, pages 88--95, Springer-Verlag, Berlin, Germany, 1988", bibdate = "Sat Dec 30 09:54:36 1995", } @Article{int:Stipp1, author = "D. Stipp", title = "{AT~\&~T} problem--solving math procedure passes early tests of its practical value", journal = "The Wallstreet Journal", year = "1985", month = "March~5,", } @TechReport{int:Stoer1, author = "J. Stoer", title = "{Innere--Punkte--Verfahren und ihre Komplexit{\"at} (I}nterior point methods and their complexity)", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:54:36 1995", } @TechReport{int:Stoer2, author = "J. Stoer", title = "Complexity bounds for interior point methods to solve linear programs", type = "{Talk held at the Symposium on Mathematical Programming in Oberwolfach, Germany}", year = "1990", month = jan, institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, West-Germany", bibdate = "Sat Dec 30 09:54:37 1995", } @TechReport{int:Stone1, author = "R. E. Stone and C. A. Tovey", title = "Karmarkar's algorithm as a generalization of simplex", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles, CA, USA}", year = "1986", month = apr, institution = "Graduate School of Business Administration, Harvard University", address = "Boston, MA~02163, USA", } @TechReport{int:Stone2, author = "R. E. Stone", title = "Karmarkar's algorithm", type = "{Unpublished Report}", year = "1985", number = "", institution = "Graduate School of Business Administration, Harvard University", address = "Boston, MA~02163, USA", } @Article{int:Stone3, author = "R. E. Stone and C. A. Tovey", title = "The simplex and projective scaling algorithms as iteratively reweighted least squares methods", journal = "SIAM Review", volume = "33", number = "2", year = "1991", month = jun, pages = "220--237", note = "Errata in {\em SIAM Review} 33(3):461, September 1991", } @TechReport{int:Stone4, author = "R. E. Stone and M. H. Wright", title = "Recent developments in linear and nonlinear programming", type = "{Short Course held at the Third SIAM Conference on Optimization in Boston, MA, USA}", year = "1989", month = apr, institution = "Graduate School of Business Administration, Harvard University", address = "Boston, MA~02163, USA", } @Article{int:Strang1, author = "G. Strang", title = "Karmarkar's algorithm in a nutshell", journal = "SIAM News", volume = "18", number = "6", year = "1985", month = nov, pages = "13", } @InBook{int:Strang2, author = "G. Strang", title = "Introduction to Applied Mathematics", chapter = "8.2~: The simplex method and {Karmarkar}'s method", year = "1986", pages = "673--689", publisher = "Wellesley--Cambridge--Press", address = "Cambridge, MA, USA", } @Article{int:Strang3, author = "G. Strang", title = "Karmarkar's algorithm and its place in applied mathematics", journal = "The Mathematical Intelligencer", volume = "9", number = "2", year = "1987", pages = "4--10", } @TechReport{int:Sun1, author = "J. Sun", title = "An affine--scaling method for linearly constrained convex programs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Industrial Engineering and Management Science, Northwestern University", address = "Evanston, IL~60208, USA", } @Article{int:Swart1, author = "E. R. Swart", title = "How {I} implemented the {Karmarkar} algorithm in one evening", journal = "APL Quote Quad", volume = "15", number = "3", year = "1985", pages = "13--16", } @TechReport{int:Swart2, author = "E. R. Swart", title = "A modified version of the {Karmarkar} algorithm", type = "{Research Report in Mathematics}", number = "98", year = "1985", institution = "Dept.\ of Mathematics and Statistics, University of Guelph", address = "Guelph, Ontario~N1G~2W1, Canada", } @PhdThesis{int:Tachat1, author = "D. Tachat", title = "Methodes int{\'{e}}rieures en programmation lin{\'{e}}aire~: {Elaboration} et mise en oeuvre de proc{\'{e}}dures de projection exacte et approch{\'{e}}e {English: Elaboration and performance of exact and approximate projection procedures}", year = "1991", school = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", note = "(In French)", bibdate = "Sat Dec 16 16:50:14 1995", } @Article{int:Tamura1, author = "A. Tamura and H. Takehara and K. Fukuda and S. Fujishige and M. Kojima", title = "A dual interior primal simplex method for linear programming", journal = "Journal of the Operations Research Society of Japan", volume = "31", year = "1988", pages = "413--429", } @Article{int:Tamura2, author = "T. E. Tamura", title = "Characteristics of {Karmarkar} method compared with {Simplex} method", journal = "Bulletin of Nagoya Institute of Technology (Nagoya, Japan)", volume = "38", year = "1986", pages = "251--256", note = "(In Japanese)", } @TechReport{int:Tan1, author = "K. C. Tan and R. M. Freund", title = "Newton's method for general parametric center problem with applications", type = "{Technical Report}", number = "RR~457", year = "1991", institution = "Dept.\ of Mathematics, National University of Singapore", address = "Singapore, India", } @InProceedings{int:Tanabe1, author = "K. Tanabe", title = "Complementarity--enforced centered {Newton} method for mathematical programming", booktitle = "New Methods for Linear Programming", editor = "K. Tone", year = "1987", pages = "118--144", address = "The Institute of Statistical Mathematics, 4-6-7~Minami Azabu, Minatoku, Tokyo~106, Japan", } @InCollection{int:Tanabe2, author = "K. Tanabe", title = "Centered {Newton} method for mathematical programming", booktitle = "System Modelling and Optimization~: Proceedings of the 13th IFIP Conference, Tokyo, Japan, Aug./Sept.~1987", editor = "M. Iri and K. Yajima", year = "1988", pages = "197--206", series = "Lecture Notes in Control and Information Sciences", volume = "113", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:37 1995", } @TechReport{int:Tanabe3, author = "K. Tanabe", title = "Centered {Newton} method for linear programming exterior point method", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "The Institute of Statistical Mathematics", address = "4-6-7~Minami Azabu, Minatoku, Tokyo~106, Japan", } @TechReport{int:Tanabe4, author = "K. Tanabe", title = "Center flattening transformation and a centered {Newton} method for linear programming", type = "{Technical Report}", year = "1987", institution = "The Institute of Statistical Mathematics", address = "4-6-7~Minami Azabu, Minatoku, Tokyo~106, Japan", } @Article{int:Tanabe5, author = "K. Tanabe and T. Tsuchiya", title = "Global analysis of dynamical systems associated with {Karmarkar}'s method for linear programming", journal = "Proceedings of the Annual Meeting of the Operations Research Society of Japan", year = "1987", pages = "132--133", } @Article{int:Tapia1, author = "R. A. Tapia", title = "Current research in numerical optimization", journal = "SIAM News", volume = "20", year = "1987", month = mar, pages = "10--11", } @TechReport{int:Tapia2, author = "R. A. Tapia", title = "Accelerating interior--point methods", type = "{Talk held at the Symposium on Mathematical Programming in Oberwolfach, Germany}", year = "1990", month = jan, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", bibdate = "Sat Dec 30 09:54:37 1995", } @TechReport{int:Tapia3, author = "R. A. Tapia and Y. Zhang", title = "A fast optimal basis identification technique for interior point linear programming methods", type = "{Technical Report}", number = "TR--89--01", year = "1989", month = apr, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", note = "Revised September 1990", } @TechReport{int:Tapia4, author = "R. A. Tapia and Y. Zhang", title = "Accelerating the convergence of interior point methods", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @Article{int:Tapia5, author = "R. A. Tapia and Y. Zhang", title = "A cubically convergent method for locating a nearby vertex in linear programming", journal = "Journal of Optimization Theory and Applications", volume = "67", year = "1990", pages = "217--225", } @TechReport{int:Tapia6, author = "R. A. Tapia and Y. Zhang", title = "A polynomial and superlinearly convergent primal--dual interior algorithm for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @Article{int:Tapia7, author = "R. A. Tapia and Y. Zhang", title = "An optimal--basis identification technique for interior--point linear programming algorithms", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "343--363", } @TechReport{int:Tapia8, author = "R. A. Tapia and Y. Zhang and M. Saltzman and R. Weiser", title = "The predictor--corrector interior--point method as a composite {Newton} method", type = "{Technical Report}", number = "TR~90--06", year = "1990", institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @Article{int:Todd1, author = "M. J. Todd", title = "A review of {N. Karmarkar}", journal = "Computing Reviews", volume = "27", year = "1986", month = mar, pages = "95--96", } @InCollection{int:Todd2, author = "M. J. Todd", title = "Polynomial algorithms for linear programming", booktitle = "Advances in Optimization and Control, Proceedings of the Conference {"Optimization Days '86"} held at Montreal, Quebec, Canada, April/May 1986", editor = "H. A. Eiselt", year = "1988", pages = "49--66", series = "Lecture Notes in Economics and Mathematical Systems", volume = "302", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:37 1995", } @Article{int:Todd3, author = "M. J. Todd", title = "Improved bounds and containing ellipsoids in {Karmarkar}'s linear programming algorithm", journal = "Mathematics of Operations Research", volume = "13", year = "1988", pages = "650--659", } @Article{int:Todd4, author = "M. J. Todd", title = "Exploiting special structure in {Karmarkar}'s algorithm for linear programming", journal = "Mathematical Programming", volume = "41", year = "1988", pages = "97--113", } @Article{int:Todd5, author = "M. J. Todd", title = "A {Dantzig--Wolfe--like variant of K}armarkar's interior--point linear programming algorithm", journal = "Operations Research", volume = "38", year = "1990", pages = "1006--1018", } @TechReport{int:Todd6, author = "M. J. Todd", title = "The effects of degeneracy and sparsity on {Karmarkar}'s projective algorithm and its variants", type = "{Technical Report}", year = "1988", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @InCollection{int:Todd7, author = "M. J. Todd", title = "Recent developments and new directions in linear programming", booktitle = "Mathematical Programming~: Recent Developments and Applications", editor = "M. Iri and K. Tanabe", year = "1989", pages = "109--157", publisher = "Kluwer Academic Press", address = "Dordrecht, The Netherlands", } @TechReport{int:Todd8, author = "M. J. Todd", title = "On {Anstreicher}'s combined phase~{I} -- phase~{II} projective algorithm for linear programming", type = "{Technical Report}", number = "776", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "To appear in {\em Mathematical Programming}", } @InCollection{int:Todd9, author = "M. J. Todd", title = "The effects of degeneracy, null and unbounded variables on variants of {Karmarkar}'s linear programming algorithm", booktitle = "Large--Scale Numerical Optimization, Papers from the Workshop held at Cornell University, Ithaca, NY, USA, October 1989", series = "SIAM Proceedings in Applied Mathematics", volume = "46", year = "1990", pages = "81--91", editor = "T. F. Coleman and Y. Li", publisher = "Society of Industrial and Applied Mathematics (SIAM)", address = "Philadelphia, PA, USA", } @Article{int:Todd10, author = "M. J. Todd", title = "The affine--scaling direction for linear programming is a limit of projective--scaling directions", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "93--105", } @TechReport{int:Todd11, author = "M. J. Todd", title = "Anticipated behavior of {Karmarkar}'s algorithm", type = "{Technical Report}", number = "879", month = dec, year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Todd12, author = "M. J. Todd", title = "Anticipated behavior of interior point methods for linear programming", type = "{Talk held at the Symposium on Mathematical Programming in Oberwolfach, Germany}", year = "1990", month = jan, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", bibdate = "Sat Dec 30 09:54:38 1995", } @TechReport{int:Todd13, author = "M. J. Todd", title = "A low complexity interior point algorithm for linear programming", type = "{Technical Report}", number = "903", year = "1990", month = apr, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "Revised August 1990", } @Article{int:Todd14, author = "M. J. Todd and B. P. Burrell", title = "An extension of {Karmarkar}'s algorithm for linear programming using dual variables", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "409--424", } @TechReport{int:Todd15, author = "M. J. Todd and C. C. Gonzaga", title = "An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine algorithm for linear programming", type = "{Talk held at the First International Symposium on Interior Point Methods for Linear Programming~: Theory and Practice, in Scheveningen, The Netherlands}", year = "1990", month = jan, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Todd16, author = "M. J. Todd and Y. Wang", title = "On combined phase~{I} -- phase~{II} projective methods for linear programming", type = "{Technical Report}", number = "877", year = "1989", month = dec, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "To appear in {\em Algorithmica}", } @Article{int:Todd17, author = "M. J. Todd and Y. Ye", title = "A centered projective algorithm for linear programming", journal = "Mathematics of Operations Research", volume = "15", year = "1990", pages = "508--529", } @TechReport{int:Todd18, author = "M. J. Todd", title = "Projected scaled steepest descent in {Kojima--Mizuno--Yoshise's} potential reduction algorithm for the linear complementarity problem", type = "{Technical Report}", number = "950", year = "1990", month = dec, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Todd19, author = "M. J. Todd", title = "Combining phase~{I} and phase~{II} in a potential reduction algorithm for linear programming", type = "{Technical Report}", number = "907", year = "1990", month = jul, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Todd20, author = "M. J. Todd and J. P. Vial", title = "Todd's low--complexity algorithm is a predictor--corrector path--following method", type = "{Technical Report}", number = "952", year = "1990", month = dec, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Todd21, author = "M. J. Todd and Y. Wang", title = "A projective algorithm for convex quadratic programming", type = "{Technical Report}", year = "1991", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @Article{int:Todd22, author = "M. J. Todd", title = "Playing with interior points", journal = "COAL Newsletter", volume = "19", year = "1991", month = aug, pages = "17--25", } @TechReport{int:Todd23, author = "M. J. Todd and S. Mizuno and Y. Ye", title = "Anticipated behavior of path--following algorithms for linear programming", type = "{Talk held at the Second Asilomar Workshop on Progress in Mathematical Programming, Asilomar, CA, USA}", year = "1990", month = feb, institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", } @TechReport{int:Todd24, author = "M. J. Todd", title = "Probabilistic models in linear programming", type = "{Technical Report}", number = "836", year = "1989", institution = "School of Operations Research and Industrial Engineering, Cornell University", address = "Ithaca, NY~14853, USA", note = "To appear in {\em Mathematics of Operations Research}", } @TechReport{int:Tolla1, author = "P. Tolla", title = "Validation numerique de l'algorithme de {Karmarkar} {(Numerical validation of Karmarkar's algorithm)}", type = "Cahier", number = "76", year = "1987", month = apr, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", note = "(In French)", } @TechReport{int:Tolla2, author = "P. Tolla", title = "Amelioration des performances de l'algorithme de {Karmarkar} dans le cas de programmes lineaires a variables bornees superieurement {(Improving the performance of Karmarkar's algorithm in linear programs with upper bounded variables)}", type = "Cahier", number = "82", year = "1987", month = nov, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", note = "(In French)", } @InCollection{int:Tolla3, author = "P. Tolla", title = "Optimal criterion and optimal solution accuracy test in {Karmarkar}'s algorithm", booktitle = "Numerical and Applied Mathematics, Part~II. Papers from the Twelfth IMACS World Congress on Scientific Computation in Paris, France, July 1988", editor = "C. Brezinski", series = "IMACS Annals of Computational and Applied Mathematics", volume = "1.2", year = "1989", pages = "629--633", publisher = "Baltzer Verlag", address = "Basel, Switzerland", } @InCollection{int:Tolla4, author = "P. Tolla", title = "Elaboration de logiciels efficaces utilisant l'algorithme de {Karmarkar} {(Elaboration of a computationally efficient utilization of Karmarkar's algorithm)}", booktitle = "New Methods in Optimization and Their Industrial Uses", editor = "J. P. Penot", series = "International Series of Numerical Mathematics", volume = "87", year = "1989", pages = "173--190", publisher = "Birkh{\"a}user Verlag", address = "Basel, Switzerland", note = "(In French)", } @TechReport{int:Tolla5, author = "P. Tolla", title = "Implementation and validation of interior point methods for linear programming", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @TechReport{int:Tolla6, author = "P. Tolla", title = "New numerical results on {Karmarkar}'s algorithm", type = "Cahier", number = "", year = "1988", institution = "Laboratoire de Analyse et Modelisation de Systemes pour l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine", address = "F-75775~Paris~Cedex~16, France", } @Article{int:Tomlin1, author = "J. A. Tomlin", title = "Experimental results with an implementation of the projective method", month = "Spring", year = "1985", } @Article{int:Tomlin2, author = "J. A. Tomlin", title = "An experimental approach to {Karmarkar}'s projective method for linear programming", journal = "Mathematical Programming Study", volume = "31", year = "1987", pages = "175--191", } @InCollection{int:Tomlin3, author = "J. A. Tomlin", title = "A note on comparing simplex and interior methods for linear programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", editor = "N. Megiddo", year = "1989", pages = "91--104", } @TechReport{int:Tomlin4, author = "J. A. Tomlin and J. S. Welch", title = "Implementing an interior point method in a mathematical programming system~: {Part~I}", type = "{Technical Report}", year = "1986", institution = "Ketron Management Science, Inc.", address = "Mountain View, CA~94040, USA", } @TechReport{int:Tomlin5, author = "J. A. Tomlin and J. S. Welch", title = "Implementing an interior point method in a mathematical programming system~: {Part~II}", type = "{Technical Report}", year = "1987", institution = "Ketron Management Science, Inc.", address = "Mountain View, CA~94040, USA", } @InProceedings{int:Tompkins1, author = "C. B. Tompkins", title = "Projection methods in calculation", booktitle = "Proceedings of the Second Symposium in Linear Programming", editor = "H. A. Antosiewicz", year = "1955", pages = "425--448", address = "U.~S.~Air Force, Washington, DC, USA", } @Article{int:Tompkins2, author = "C. B. Tompkins", title = "Some methods of computational attack on programming problems, other than the simplex method", journal = "Naval Research Logistics Quarterly", volume = "4", year = "1957", pages = "95--96", } @TechReport{int:Tone1, author = "K. Tone", title = "A hybrid method for linear programming", type = "{Technical Report}", number = "85--B--1", year = "1985", institution = "Graduate School for Policy Science, Saitama University", address = "Urawa, Saitama~338, Japan", } @TechReport{int:Tone2, author = "K. Tone", title = "An implementation of a revised {Karmarkar} method", type = "{Technical Report}", year = "1986/87", institution = "Graduate School for Policy Science, Saitama University", address = "Urawa, Saitama~338, Japan", } @Article{int:Tone3, author = "K. Tone", title = "Linear programming and {Karmarkar} patents", journal = "Systems, Control and Information", volume = "34", number = "5", year = "1990", month = apr, pages = "209--215", note = "(In Japanese)", } @TechReport{int:Tone4, author = "K. Tone", title = "An {$O(\sqrt{n}L)$} iteration large--step logarithmic barrier function algorithm for linear programming", type = "{Research Report}", number = "89--B--5", year = "1989", institution = "Graduate School for Policy Science, Saitama University", address = "Urawa, Saitama~338, Japan", } @TechReport{int:Tone5, author = "K. Tone", title = "An active--set strategy in interior point method for linear programming", type = "{Working Paper}", year = "1991", institution = "Graduate School for Policy Science, Saitama University", address = "Urawa, Saitama~338, Japan", } @TechReport{int:Torabi1, author = "M. Torabi", title = "Decomposed block {Cholesky} factorization in the {Karmarkar} algorithm~: {A} proposed scheme for solving a class of super large {LP} problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @Article{int:Torabi2, author = "M. Torabi", title = "Decomposed block {Cholesky} factorization in the {Karmarkar} algorithm.~{Solving} a class of super large {LP} problems", journal = "Computers and Mathematics with Applications", volume = "20", number = "2", year = "1990", pages = "1--7", } @TechReport{int:Tovey1, author = "C. A. Tovey", title = "Integrating {Karmarkar}'s algorithm into the curriculum", type = "{Workshop held at the ORSA/TIMS Joint National Meeting in Miami Beach, FL, USA}", year = "1986", month = oct, institution = "School of Industrial and Systems Engineering, Georgia Technology Institute", address = "Atlanta, GA~30322-0205, USA", } @Article{int:Tovey2, author = "C. A. Tovey", title = "The challenge~: {Teaching K}armarkar's algorithm", journal = "OR/MS Today", volume = "15", number = "2", year = "1988", month = apr, pages = "18--19", } @TechReport{int:Trafalis1, author = "T. B. Trafalis and T. L. Morin", title = "Interior point methods in multiobjective convex optimization", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "School of Industrial Engineering, University of Oklahoma", address = "Norman, OK~73019, USA", } @PhdThesis{int:Trafalis2, author = "T. B. Trafalis", title = "Efficient faces of a polytope~: {Interior} methods in multiple objective optimization", year = "1989", month = aug, school = "Dept.\ of Mathematics and Computer Science, School of Industrial Engineering, Purdue University", address = "West Lafayette, IN~47907, USA", } @TechReport{int:Trafalis3, author = "T. B. Trafalis", title = "Interior point methods in backpropagation neural networks", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "School of Industrial Engineering, University of Oklahoma", address = "Norman, OK~73019, USA", } @Article{int:Tseng1, author = "P. Tseng", title = "A simple complexity proof for a polynomial--time linear programming algorithm", journal = "Operations Research Letters", volume = "8", year = "1989", pages = "155--159", } @TechReport{int:Tseng2, author = "P. Tseng", title = "Global linear convergence of a path following algorithm for some variational inequality problems", type = "{Working Paper}", year = "1990", institution = "Dept.\ of Mathematics, GN--50, University of Washington", address = "Seattle, WA, USA", } @TechReport{int:Tseng3, author = "P. Tseng and Z. Q. Luo", title = "On the convergence of the affine--scaling algorithm", type = "{Technical Report}", number = "CICS--P--169", year = "1989", institution = "Center for Intelligent Control Systems, Massachusetts Institute of Technology", address = "Cambridge, MA~02139, USA", } @TechReport{int:Tsuchiya1, author = "T. Tsuchiya", title = "Global convergence of the affine--scaling methods for degenerate linear programming problems", type = "{Research Memorandum}", number = "373", year = "1989", institution = "The Institute of Statistical Mathematics", address = "4-6-7 Minami-Azabu, Minato-ku, Tokyo~106, Japan", note = "Revised January 1991. To appear in {\em Mathematical Programming, Series~B, 1991}", } @Article{int:Tsuchiya2, author = "T. Tsuchiya and K. Tanabe", title = "Local convergence properties of new methods in linear programming", journal = "Journal of the Operations Research Society of Japan", volume = "33", year = "1990", pages = "22--45", } @Article{int:Tsuchiya3, author = "T. Tsuchiya", title = "Degenerate linear programming problems and the affine scaling method", journal = "Systems, Control and Information", volume = "34", number = "5", year = "1990", month = apr, pages = "216--222", note = "(In Japanese)", } @Article{int:Tsuchiya4, author = "T. Tsuchiya", title = "On {Yamashita's method and Freund's method} for linear programming", journal = "Cooperative Research Report of the Institute of Statistical Mathematics", volume = "10", year = "1988", pages = "105--115", note = "(In Japanese)", } @Article{int:Tsuchiya5, author = "T. Tsuchiya", title = "Dual standard form linear programming problems and {Karmarkar}'s canonical form", journal = "Lecture Note of the Research Institute of Statistical Mathematics", volume = "676", year = "1988", pages = "330--336", note = "(In Japanese)", } @TechReport{int:Tsuchiya6, author = "T. Tsuchiya", title = "Global convergence property of the affine scaling method for primal degenerate linear programming problems", type = "{Research Memorandum}", number = "367", year = "1989", month = aug, institution = "The Institute of Statistical Mathematics", address = "4-6-7~Minami-Azabu, Minato-ku, Tokyo~106, Japan", note = "Revised September 1990. To appear in {\em Mathematics of Operations Research}", } @TechReport{int:Tsuchiya7, author = "T. Tsuchiya", title = "Local analysis of {Iri and Imai's} method for degenerate linear programming problems", type = "{Research Memorandum (in preparation)}", year = "1991", institution = "The Institute of Statistical Mathematics", address = "4-6-7~Minami-Azabu, Minato-ku, Tokyo~106, Japan", } @TechReport{int:Tsuchiya8, author = "T. Tsuchiya", title = "Quadratic convergence of {Iri and Imai's} method for degenerate linear programming problems", type = "{Research Memorandum}", number = "412", year = "1991", institution = "The Institute of Statistical Mathematics", address = "4-6-7~Minami-Azabu, Minato-ku, Tokyo~106, Japan", } @PhdThesis{int:Tsuchiya9, author = "T. Tsuchiya", title = "A study on global and local convergence of interior point algorithms for linear programming", year = "1991", school = "Faculty of Engineering, The University of Tokyo", address = "Tokyo, Japan", note = "(In Japanese)", } @TechReport{int:Turner1, author = "K. Turner", title = "A variable metric variant of the {Karmarkar} algorithm for linear programming", type = "{Technical Report}", number = "TR--87--13", year = "1987", institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @Article{int:Turner2, author = "K. Turner", title = "Computing projections for the {Karmarkar} algorithm", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "141--154", } @TechReport{int:Vaidya1, author = "P. M. Vaidya", title = "Linear programming and the center of a polytope", type = "{Technical Report}", year = "1988", institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @InCollection{int:Vaidya2, author = "P. M. Vaidya", title = "A locally well--behaved potential function and a simple {Newton}--type method for finding the center of a polytope", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", editor = "N. Megiddo", year = "1989", pages = "79--90", } @TechReport{int:Vaidya3, author = "P. M. Vaidya", title = "A new algorithm for minimizing a convex function over convex sets", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Vaidya4, author = "P. M. Vaidya", title = "An algorithm for linear programming which requires ${O((m + n)n^2 + (m + n)^{1.5}nL)}$ arithmetic operations", journal = "Mathematical Programming", volume = "47", year = "1990", pages = "175--201", note = "Condensed version in~: {\em Proceedings of the 19th Annual ACM Symposium on Theory of Computing}, pages 29--38, 1987", } @InCollection{int:Vaidya5, author = "P. M. Vaidya", title = "Reducing the parallel complexity of certain linear programming problems", booktitle = "Proceedings of the 31st Annual Symposium on Foundations of Computer Science, St.~Louis, MO, USA, October 1990", year = "1990", pages = "583--589", publisher = "IEEE Computer Society Press", address = "Los Alamitos, CA, USA", } @InCollection{int:Vaidya6, author = "P. M. Vaidya", title = "Speeding--up linear programming using fast matrix multiplication", booktitle = "Proceedings of the 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 1989", year = "1990", pages = "332--337", publisher = "IEEE Computer Society Press", address = "Los Alamitos, CA, USA", } @InCollection{int:Vaidya7, author = "P. M. Vaidya", title = "A new algorithm for minimizing a convex function over convex sets", booktitle = "Proceedings of the 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 1989", year = "1990", pages = "338--343", publisher = "IEEE Computer Society Press", address = "Los Alamitos, CA, USA", } @TechReport{int:Vanderbei1, author = "R. J. Vanderbei", title = "A rescaled orthant variant of {Karmarkar}'s algorithm", type = "{Technical Report}", year = "1986", institution = "AT~\&~T Bell Laboratories", address = "Holmdel, NJ~07733, USA", } @TechReport{int:Vanderbei2, author = "R. J. Vanderbei", title = "The affine--scaling algorithm and primal degeneracy", type = "{Talk held at the Second Asilomar Workshop on Progress in Mathematical Programming, Asimolar Conference Center, Pacific Grove, CA, USA}", year = "1987", institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Misc{int:Vanderbei3, author = "R. J. Vanderbei", title = "Methods and apparatus for efficient resource allocation", howpublished = "U.S.~Patent No.~4.744.026", year = "1988", note = "AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA", } @Article{int:Vanderbei4, author = "R. J. Vanderbei", title = "Affine--scaling for linear programs with free variables", journal = "Mathematical Programming", volume = "43", year = "1989", pages = "31--44", } @TechReport{int:Vanderbei5, author = "R. J. Vanderbei", title = "New developments in the affine--scaling algorithm for {LP}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @InCollection{int:Vanderbei6, author = "R. J. Vanderbei and J. C. Lagarias", title = "{I. I. Dikin's} convergence result for the affine--scaling algorithm", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "109--119", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @Article{int:Vanderbei7, author = "R. J. Vanderbei and M. S. Meketon and B. A. Freedman", title = "A modification of {Karmarkar}'s linear programming algorithm", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "395--407", } @TechReport{int:Vanderbei8, author = "R. J. Vanderbei", title = "Efficient handling of dense columns in linear and quadratic programs", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "AT~\&~T Bell Laboratories", address = "10~Knob Hill Road, Morganville, NJ~07751, USA", } @Article{int:Vanderbei9, author = "R. J. Vanderbei", title = "Splitting dense columns in sparse linear systems", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "107--117", } @TechReport{int:Vanderbei10, author = "R. J. Vanderbei", title = "Symmetric quasi--definite matrices", type = "{Technical Report}", number = "SOL~91--10", year = "1991", institution = "Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Vanderbei11, author = "R. J. Vanderbei and T. J. Carpenter", title = "Symmetric indefinite systems for interior point methods", type = "{Technical Report}", number = "SOR~91--7", year = "1991", institution = "Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @TechReport{int:Vanderbei12, author = "R. J. Vanderbei", title = "{ALPO~: Another linear program solver}", type = "{Manuscript}", year = "1990", institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", note = "Revised May 1991, Dept.\ of Civil Engineering and Operations Research, Princeton University, Princeton, NJ~08544, USA", } @TechReport{int:Vanderbei13, author = "R. J. Vanderbei", title = "{Performance of the AT~\&~T KORBX System}", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Vanderbei14, author = "R. J. Vanderbei", title = "{A brief description of ALPO}", type = "{Technical Report}", year = "1990", institution = "AT~\&~T Bell Laboratories", address = "Murray Hill, NJ~07974, USA", note = "To appear in {\em Operations Research Letters, 1991}", } @TechReport{int:Vanderbei15, author = "R. J. Vanderbei", title = "Dense columns and interior--point methods for {LP}", type = "{Manuscript}", year = "1991", institution = "Dept.\ of Civil Engineering and Operations Research, Princeton University", address = "Princeton, NJ~08544, USA", } @InProceedings{int:Vannelli1, author = "A. Vannelli", title = "An interior point method for solving the global routing problem", booktitle = "Proceedings of the IEEE Custom Integrated Circuits Conference, San Diego, CA, USA, May 1988", year = "1989", pages = "3.4.1--3.4.4", } @TechReport{int:Vannelli2, author = "A. Vannelli and E. Klein", title = "A {Cholesky}--conjugate gradient implementation of {Karmarkar}'s algorithm", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Faculty of Engineering, Dept.\ of Electrical Engineering, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", } @Article{int:Vannelli3, author = "A. Vannelli", title = "An adaptation of the interior point method for solving the global routing problem", journal = "IEEE Transactions on Computer--Aided Design of Integrated Circuits and Systems", volume = "10", number = "2", year = "1991", month = feb, pages = "193--203", } @Article{int:Venkaiah1, author = "V. C. Venkaiah", title = "An efficient algorithm for linear programming", journal = "Proceedings of the Indian Academy of Sciences, Mathematical Sciences", volume = "100", year = "1990", pages = "205--301", } @InCollection{int:Vial1, author = "J. P. Vial", title = "Approximate projections in a projective method for the linear feasibility problem", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", editor = "N. Megiddo", year = "1989", pages = "65--78", } @Article{int:Vial2, author = "J. P. Vial", title = "A Fully Polynomial-Time Projective Method", journal = "Operations Research Letters", volume = "7", year = "1988", pages = "15--19", } @InCollection{int:Vial3, author = "J. P. Vial", title = "A unified approach to projective algorithms for linear programming", booktitle = "Optimization~: Proceedings of the 5th French--German Conference in Castel--Novel, Varetz, France, October 1988", editor = "S. Dolecki", year = "1989", pages = "191--220", series = "Lecture Notes in Mathematics", volume = "1405", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:38 1995", } @InCollection{int:Vial4, author = "J. P. Vial", title = "Decomposition of structured linear programs based on analytic centers", year = "1991", pages = "190--203", series = "Lecture Notes in Economics and Mathematical Systems", volume = "353", publisher = "Springer-Verlag", address = "Berlin, Germany", bibdate = "Sat Dec 30 09:54:38 1995", } @InCollection{int:Vorst1, author = "{J. G. G. van de} Vorst", title = "An attempt to use parallel computing in large scale optimisation", booktitle = "Logistics, Where Ends Have to Meet~: Proceedings of the Shell Conference on Logistics in Apeldoorn, The Netherlands, November 1988", editor = "{C. F. H. van} Rijn", year = "1989", pages = "112--119", publisher = "Pergamon Press", address = "Oxford, United Kingdom", } @TechReport{int:Vucetic1, author = "V. Vucetic", title = "Active set strategies in linear programming using barrier functions", type = "{Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de Janeiro, Brazil}", year = "1991", month = jul, institution = "Energoinvest--Sou", address = "Tvornicka~3, YU-71000~Sarajevo, Yugoslavia", } @InProceedings{int:Wanka1, author = "A. Wanka", title = "Interior and exterior methods for linear programming", booktitle = "Operations Research Proceedings 1988", editor = "D. Pressmar and K. E. Jaeger and H. Krallmann and H. Schellhaas and L. Streitfeldt", year = "1989", pages = "214--221", address = "Springer-Verlag, Berlin, Germany", bibdate = "Sat Dec 30 09:54:38 1995", } @Article{int:Wei1, author = "Z. L. Wei", title = "An exact solution to linear programming using an interior point method", journal = "Journal of Computational Mathematics", volume = "5", year = "1987", pages = "264--271", } @Article{int:Wei2, author = "Z. L. Wei", title = "An interior point method for linear programming", journal = "Journal of Computational Mathematics", volume = "5", year = "1987", pages = "342--351", } @Article{int:Wei3, author = "Z. L. Wei", title = "Some recent developments in linear programming", journal = "Mathematics in Practice and Theory", volume = "3", year = "1988", pages = "82--89", note = "(In Chinese)", } @InBook{int:Werner1, author = "J. Werner", title = "Numerische Mathematik~2 (Numerical Mathematics~2)", chapter = "6.4~: {Das Karmarkar Verfahren (The Karmarkar algorithm)}", year = "1992", pages = "128--141", publisher = "Vieweg Verlag", address = "Braunschweig, Germany", } @TechReport{int:Whisman1, author = "A. W. Whisman", title = "Optimization modelling in the military airlift command", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "CINCMAC Analysis Group, HQ~MAC/AG", address = "Scott AFB, IL~62225, USA", } @TechReport{int:White1, author = "D. J. White", title = "Linear programming and {Huard}'s method of centres", type = "{Working Paper}", year = "1989", institution = "Universities of Manchester and Virginia", address = "Manchester, United Kingdom", } @TechReport{int:Williams1, author = "R. O. Williams", title = "An implementation of the affine scaling algorithm for linear programming problems with network constraints", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Management Science, California State University", address = "Northridge, Los Angeles, CA~90024, USA", } @TechReport{int:Wilson1, author = "J. Wilson", title = "A barrier function approach to mixed integer programming", type = "{Talk held at the Symposium APMOD~'91---Applied Mathematical Programming and Modelling, Brunel University, London, UK}", year = "1991", month = jan, institution = "Loughborough University", address = "Loughborough, UK", } @InCollection{int:Witzgall1, author = "C. Witzgall and P. T. Boggs and P. D. Domich", title = "On the convergence behavior of trajectories for linear programming", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "161--187", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Witzgall2, author = "C. Witzgall and P. T. Boggs and P. D. Domich", title = "On center trajectories and their relatives in linear programming", type = "{NISTIR Technical Report (in preparation)}", year = "1991", institution = "United States Department of Commerce, Applied and Computational Mathematics Division, National Institute of Standards and Technology", address = "Gaithersburg, MD~20899, USA", note = "First draft in April 1988", } @TechReport{int:Wolkowicz1, author = "H. Wolkowicz and A. {Ben--Israel}", title = "A volume and constraint reducing algorithm for linear programming", type = "{Technical Report}", year = "1986", institution = "Dept.\ of Combinatorics and Optimization, University of Waterloo", address = "Waterloo, Ontario~N2L~3G1, Canada", } @TechReport{int:Wright1, author = "M. H. Wright", title = "Issues of numerical analysis in barrier trajectory methods", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Wright2, author = "M. H. Wright", title = "Interior methods for nonlinearly constrained optimization", type = "{Talk held at the SIAM Annual Meeting in Chicago, IL, USA}", year = "1990", month = jul, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Wright3, author = "S. J. Wright", title = "An interior point algorithm for linearly constrained optimization", type = "{Technical Report}", number = "MCS--P162--0790", year = "1990", month = jul, institution = "Mathematical and Computer Science Division, Argonne National Laboratory", address = "Argonne, IL~60439, USA", } @TechReport{int:Wright4, author = "M. H. Wright", title = "Strategies in path--following methods for nonlinear constraints", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Wright5, author = "M. H. Wright", title = "Linear algebra issues in interior methods", type = "{Talk held at the Fourth SIAM Conference on Applied Linear Algebra in Minneapolis, MN, USA}", year = "1991", month = sep, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @Article{int:Wright6, author = "M. H. Wright", title = "A brief history of linear programming", journal = "SIAM News", volume = "18", number = "3", year = "1985", month = nov, pages = "4", } @TechReport{int:Wright7, author = "M. H. Wright", title = "Interior methods for constrained optimization", type = "{Numerical Analysis Manuscript}", number = "91--10", year = "1991", month = nov, institution = "AT~\&~T~Bell Laboratories", address = "Murray Hill, NJ~07974, USA", } @TechReport{int:Xiao1, author = "D. Xiao", title = "Fractional linear functions and the analysis of variants of {Karmarkar}'s method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Xiao2, author = "D. Xiao and D. Goldfarb", title = "A primal projective interior point method for linear programming", type = "{Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver, British Columbia, Canada}", year = "1989", month = may, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Xiao3, author = "D. Xiao and D. Goldfarb", title = "A path--following projective interior point method for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Xiao4, author = "D. Xiao and D. Goldfarb", title = "On the complexity of a class of projective interior point methods", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @TechReport{int:Yamashita1, author = "H. Yamashita", title = "A polynomially and quadratically convergent method for linear programming", type = "{Working Paper}", year = "1986", institution = "Mathematical Systems Institute, Inc.", address = "Tokyo, Japan", } @TechReport{int:Yamashita2, author = "H. Yamashita", title = "A class of primal dual method for constrained optimization", type = "{Working Paper}", year = "1991", institution = "Mathematical Systems Institute, Inc.", address = "Tokyo, Japan", } @TechReport{int:Yang1, author = "E. K. Yang and W. S. Hwang", title = "An interior point method for dynamic {Leontief} type linear programs", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV, USA}", year = "1990", month = may, institution = "Institute of Applied Mathematics, Tsing Hua University", address = "Hsinchu, 30043, People Republic of China", } @TechReport{int:Ye1, author = "Y. Ye", title = "A large group of projections for linear programming", type = "{Working Paper}", year = "1985", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ye2, author = "Y. Ye", title = "Cutting current--objective method in projective algorithm for linear programming", type = "{Working Paper}", year = "1985", month = feb, institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ye3, author = "Y. Ye", title = "Cutting--objective and scaling methods---a polynomial algorithm for linear programming", type = "{Working Paper}", year = "1985", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", note = "Submitted to {\em Mathematical Programming}", } @TechReport{int:Ye4, author = "Y. Ye", title = "Barrier projection and sliding current objective method for linear programming", type = "{Talk held at the 12th Mathematical Programming Symposium, Boston, MA, USA}", year = "1985", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @PhdThesis{int:Ye5, author = "Y. Ye", title = "Interior algorithms for linear, quadratic, and linearly constrained convex programming", year = "1987", school = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ye6, author = "Y. Ye", title = "Dual approach of {Karmarkar}'s algorithm and the ellipsoid method", type = "{Working Paper}", year = "1987", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ye7, author = "Y. Ye", title = "Further development on the interior algorithm for convex quadratic programming", type = "{Working Paper}", year = "1987", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Ye8, author = "Y. Ye", title = "Karmarkar's algorithm and the ellipsoid method", journal = "Operations Research Letters", volume = "6", year = "1987", pages = "177--182", } @Article{int:Ye9, author = "Y. Ye", title = "An ${O(n^{3}L)}$ potential reduction algorithm for linear programming", journal = "Mathematical Programming", volume = "50", year = "1991", pages = "239--258", } @TechReport{int:Ye10, author = "Y. Ye", title = "The `build-down' scheme for path-following algorithms", type = "{Technical Report}", year = "1988", institution = "Integrated Systems Inc.", address = "Santa Clara, CA, USA", } @TechReport{int:Ye11, author = "Y. Ye", title = "A class of potential functions for linear programming", type = "Management Science Working Paper", number = "88--13", year = "1988", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye12, author = "Y. Ye", title = "Potential functions and polytopes", type = "{Talk held at the ORSA/TIMS Joint National Meeting in New York, NY, USA}", year = "1989", month = oct, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye13, author = "Y. Ye", title = "Eliminating columns and rows in potential reduction and path--following algorithms for linear programming", type = "{Working Paper Series}", number = "89--7", year = "1989", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @InCollection{int:Ye14, author = "Y. Ye", title = "An extension of {Karmarkar}'s algorithm and the trust region method for quadratic programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer-Verlag", address = "New York, NY, USA", editor = "N. Megiddo", year = "1989", pages = "49--64", } @TechReport{int:Ye15, author = "Y. Ye", title = "Comparative analysis of affine scaling algorithms based on simplifying assumptions", type = "{Technical Report}", year = "1990", month = jan, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", note = "Revised November 1990. To appear in {\em Mathematical Programming, Series~B, 1991}", } @Article{int:Ye16, author = "Y. Ye", title = "A `build-down' scheme for linear programming", journal = "Mathematical Programming", volume = "46", year = "1990", pages = "61--72", } @Article{int:Ye17, author = "Y. Ye", title = "A class of projective transformations for linear programming", journal = "SIAM Journal on Computing", volume = "19", year = "1990", pages = "457--466", } @Article{int:Ye18, author = "Y. Ye", title = "Recovering optimal basic variables in {Karmarkar}'s polynomial algorithm for linear programming", journal = "Mathematics of Operations Research", volume = "15", year = "1990", pages = "564--572", } @TechReport{int:Ye19, author = "Y. Ye", title = "Complexity analysis on {Karmarkar}'s algorithm", type = "{Manuscript}", year = "1990", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @Article{int:Ye20, author = "Y. Ye and M. Kojima", title = "Recovering optimal dual solutions in {Karmarkar}'s polynomial algorithm for linear programming", journal = "Mathematical Programming", volume = "39", year = "1987", pages = "305--317", } @Article{int:Ye21, author = "Y. Ye and P. M. Pardalos", title = "A class of linear complementarity problems solvable in polynomial time", journal = "Linear Algebra and Its Applications", volume = "152", year = "1991", pages = "3--17", } @Article{int:Ye22, author = "Y. Ye and M. J. Todd", title = "Containing and shrinking ellipsoids in the path--following algorithm", journal = "Mathematical Programming", volume = "47", year = "1990", pages = "1--10", } @TechReport{int:Ye23, author = "Y. Ye and E. Tse", title = "A polynomial--time algorithm for convex quadratic programming", type = "{Working Paper}", year = "1986", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @Article{int:Ye24, author = "Y. Ye and E. Tse", title = "An extension of {Karmarkar}'s projective algorithm for convex quadratic programming", journal = "Mathematical Programming", volume = "44", year = "1989", pages = "157--179", } @TechReport{int:Ye25, author = "Y. Ye", title = "A further result on the potential reduction algorithm for the {$P$}--matrix linear complementarity problem", type = "{Working Paper}", year = "1988", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @Article{int:Ye26, author = "Y. Ye", title = "Interior point algorithms for global optimization", journal = "Annals of Operations Research", volume = "25", year = "1990", pages = "59--74", } @TechReport{int:Ye27, author = "Y. Ye", title = "Interior point algorithms for quadratic programming", type = "{Working Paper Series}", number = "89--29", year = "1989", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", note = "To appear in S. Kumar, editor, {\em Recent Developments in Mathematical Programming}, Gordon~\& Beach Scientific Publishers, 1991", } @TechReport{int:Ye28, author = "Y. Ye", title = "Line searches in potential reduction algorithm for linear programming", type = "Manuscript", year = "1989", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye29, author = "Y. Ye", title = "On an affine scaling algorithm for nonconvex quadratic programming", type = "{Technical Report}", year = "1988", month = apr, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", note = "Revised July 1989", } @TechReport{int:Ye30, author = "Y. Ye", title = "A fully polynomial--time approximation algorithm for computing a stationary point of the generalized linear complementarity problem", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye31, author = "Y. Ye", title = "Further developments in potential reduction algorithm", type = "{Technical Report}", year = "1989", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye32, author = "Y. Ye", title = "Bimatrix equilibrium points and potential functions", type = "{Technical Report}", year = "1988", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye33, author = "Y. Ye", title = "A combinatorial property of analytic centers of polytopes", type = "{Technical Report}", year = "1989", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye34, author = "Y. Ye", title = "Anticipated behavior of affine scaling algorithms for linear programming", type = "{Technical Report}", year = "1990", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye35, author = "Y. Ye", title = "On the finite convergence of interior--point algorithms for linear programming", type = "{Technical Report}", number = "91--05", year = "1991", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye36, author = "Y. Ye and S. S. Chiu", title = "Recovering the shadow price in projection methods for linear programming", type = "{Technical Report}", year = "1985", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye37, author = "Y. Ye and F. A. Potra", title = "An interior--point algorithm for solving entropy optimization problems with globally linear and locally quadratic convergence rate", type = "{Working Paper Series}", number = "90--22", year = "1990", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye38, author = "Y. Ye", title = "On the interior algorithms for nonconvex quadratic programming", type = "{Manuscript}", year = "1988", institution = "Integrated Systems, Inc.", address = "Santa Clara, CA, USA", } @InCollection{int:Ye39, author = "Y. Ye", title = "An {$O(n^{3}L)$} potential reduction algorithm for linear programming", booktitle = "Mathematical Developments Arising from Linear Programming~: Proceedings of a Joint Summer Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July 1988", editor = "J. C. Lagarias and M. J. Todd", year = "1990", pages = "77--88", series = "Contemporary Mathematics", volume = "114", publisher = "American Mathematical Society", address = "Providence, Rhode Island, USA", } @TechReport{int:Ye40, author = "Y. Ye", title = "A `build-down' simplex --- {Karmarkar} method for linear programming", type = "{Technical Report}", year = "1987", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ye41, author = "Y. Ye", title = "A potential reduction algorithm allowing column generation", type = "{Working Paper}", year = "1989", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye42, author = "Y. Ye and K. O. Kortanek and J. A. Kaliski and S. Huang", title = "Near--boundary behavior of primal--dual potential reduction algorithms for linear programming", type = "{Working Paper}", year = "1990", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye43, author = "Y. Ye and O. G{\"u}ler and R. A. Tapia and Y. Zhang", title = "A quadratically convergent ${O(\sqrt{n}L)}$--iteration algorithm for linear programming", type = "{Technical Report}", number = "TR--91--26", year = "1991", month = aug, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Ye44, author = "Y. Ye and R. A. Tapia and Y. Zhang", title = "A superlinearly convergent ${O(\sqrt{n}L)}$--iteration algorithm for linear programming", type = "{Technical Report}", number = "TR--91--22", year = "1991", institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Ye45, author = "Y. Ye", title = "Toward probabilistic analysis of interior--point algorithms for linear programming", type = "{Working Paper Series}", number = "91--13", year = "1991", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye46, author = "Y. Ye", title = "K--projection and cutting--objective method for linear programming", type = "{Talk held at the 12th Mathematical Programming Symposium, Boston, MA, USA}", year = "1985", institution = "Dept.\ of Engineering Economic Systems, Stanford University", address = "Stanford, CA~94305, USA", } @TechReport{int:Ye47, author = "Y. Ye and J. A. Kaliski", title = "Further results on build--up approaches for linear programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in, Anaheim, CA, USA}", year = "1991", month = nov, institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @TechReport{int:Ye48, author = "Y. Ye", title = "The potential algorithm for linear complementarity problems", type = "{Technical Report}", year = "1998", institution = "Dept.\ of Management Science, University of Iowa", address = "Iowa City, IA~52242, USA", } @PhdThesis{int:Yeh1, author = "Q. J. Yeh", title = "A reduced dual affine scaling algorithm for solving assignment and transportation problems", year = "1989", school = "Dept.\ of Industrial Engineering and Operations Research, Columbia University", address = "New York, NY~10027, USA", } @Article{int:Zaijan1, author = "D. Zaijan", title = "A modified {Karmarkar}'s algorithm", journal = "Applied Mathematics---A Journal of Chinese Universities", volume = "3", year = "1988", pages = "41--56", } @TechReport{int:Zhang1, author = "Y. Zhang and R. A. Tapia and J. E. Dennis", title = "On the superlinear and quadratic convergence of primal--dual interior point linear programming algorithms", type = "{Technical Report}", number = "TR~90--6", year = "1990", month = jan, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Zhang2, author = "Y. Zhang and R. A. Tapia and F. Potra", title = "On the superlinear convergence of interior point algorithms for a general class of problems", type = "{Technical Report}", number = "TR~90--9", year = "1990", month = mar, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Zhang3, author = "Y. Zhang and R. A. Tapia", title = "A polynomial--time and superlinearly convergent interior point algorithm for linear programming", type = "{Technical Report}", year = "1991", month = mar, institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Zhang4, author = "S. Zhang", title = "On the convergence property of {Iri--Imai's} method for linear programming", type = "{Technical Report}", number = "8917/A", year = "1989", institution = "Economic Institute, Erasmus University", address = "Rotterdam, The Netherlands", } @TechReport{int:Zhang5, author = "Y. Zhang", title = "Super--linear convergence of interior point algorithms for a class of mathematical programming problems", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Nashville, Tennessee, USA}", year = "1991", month = may, institution = "Dept.\ of Mathematics \& Statistics, University of Maryland Baltimore County", address = "Baltimore, MD~21228, USA", } @Article{int:Zhang6, author = "J. Z. Zhang", title = "The affine transformation method and the path following method for solving linear programming problems", journal = "Chinese Journal of Operations Research", volume = "8", number = "2", year = "1989", pages = "25--34", note = "(In Chinese)", } @TechReport{int:Zhang7, author = "Y. Zhang and R. A. Tapia", title = "A quadratically convergent polynomial primal--dual interior--point algorithm for linear programming", type = "{Technical Report}", number = "TR~90--40", year = "1990", institution = "Dept.\ of Mathematical Sciences, Rice University", address = "Houston, TX~77251, USA", } @TechReport{int:Zhao1, author = "G. Zhao and J. Stoer", title = "Estimating the complexity of path following methods for solving linear programs by curvature integrals", type = "{Technical Report}", number = "225", year = "1990", institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Am Hubland, D-8700~W{\"u}rzburg, Germany", bibdate = "Sat Dec 30 09:54:40 1995", } @Article{int:Zheng1, author = "Q. Zheng", title = "On the complexity of linear programming problems", journal = "Chinese Journal of Operations Research", volume = "7", number = "2", year = "1988", pages = "1--10", note = "(In Chinese)", } @Article{int:Zhou1, author = "J. Zhou and N. Xu and W. Chen", title = "Discussion on {Karmarkar}'s method for solving unstandard model", journal = "Journal of Southeastern University (Nanjing, PR China), English Edition", volume = "5", number = "1", year = "1989", pages = "38--45", note = "", } @TechReport{int:Zhu1, author = "J. Zhu and K. O. Kortanek", title = "A polynomial path--following algorithm for linearly constrained convex programming", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, USA}", year = "1990", month = oct, institution = "College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @TechReport{int:Zhu2, author = "J. Zhu", title = "A path following algorithm for a class of convex programming problems", type = "{Working Paper Series}", number = "90--14", year = "1990", institution = "College of Business Administration, University of Iowa", address = "Iowa City, IA~52240, USA", } @TechReport{int:Zikan1, author = "K. Zikan and R. W. Cottle", title = "The box method for linear programming, part~{I~: B}asic theory", type = "{Technical Report}", year = "1987", institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305-4022, USA", } @TechReport{int:Zikan2, author = "K. Zikan and R. W. Cottle", title = "The box method for linear programming, part~{II~: T}reatment of problems in standard form with explicitly bounded variables", type = "{Technical Report}", year = "1987", institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305-4022, USA", } @TechReport{int:Zikan3, author = "K. Zikan and R. W. Cottle", title = "Solving linear programs with the box method", type = "{Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC, USA}", year = "1988", month = apr, institution = "Systems Optimization Laboratory, Dept.\ of Operations Research, Stanford University", address = "Stanford, CA~94305-4022, USA", } @InCollection{int:Zimmermann1, author = "U. Zimmermann", title = "On recent developments in linear programming", booktitle = "Trends in Mathematical Optimization~: Proceedings of the 4th French--German Conference on Optimization in Irsee, Germany, April 1986", editor = "K. H. Hoffmann and J. B. Hiriat--Urruty and C. Lemarechal and J. Zowe", series = "International Series of Numerical Mathematics", volume = "84", year = "1988", pages = "353--390", publisher = "Birkh{\"a}user Verlag", address = "Basel, Switzerland", bibdate = "Sat Dec 30 09:54:40 1995", } @TechReport{int:Zimmermann2, author = "U. Zimmermann", title = "Search directions for projective methods", type = "{Technical Report}", year = "1989", month = feb, institution = "Technische Universit{\"a}t Braunschweig, Institut f{\"u}r Angewandte Mathematik, Abt.\ f{\"u}r Math.\ Optimierung", address = "Pockelstr.~14, D-3300~Braunschweig, Germany", } @Article{int:Zimmermann3, author = "U. Zimmermann", title = "Search directions for a class of projective methods", journal = "Zeitschrift f{\"u}r Operations Research---Methods and Models of Operations Research", volume = "34", year = "1990", pages = "353--379", } @TechReport{int:Zimmermann4, author = "U. Zimmermann and C. Wallacher", title = "An interior point method for flow problems", type = "{Talk held at the DGOR--Jahrestagung in Vienna, Austria}", year = "1990", month = aug, institution = "Technische Universit{\"a}t Braunschweig, Institut f{\"u}r Angewandte Mathematik, Abt.\ f{\"u}r Math.\ Optimierung", address = "Pockelstr.~14, D-3300~Braunschweig, Germany", bibdate = "Sat Dec 30 09:54:40 1995", }