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K.~M. Anstreicher.
\newblock A combined phase\,{I}\,--\,phase\,{II} projective algorithm for
linear programming.
\newblock {\em Mathematical Programming}, 43:209--223, 1989.
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K.~M. Anstreicher.
\newblock Progress in interior point algorithms since 1984.
\newblock {\em SIAM News}, 22:12--14, March 1989.
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K.~M. Anstreicher.
\newblock Recent developments in algorithms for linear programming.
\newblock {Talk held at the Third SIAM Conference on Optimization in Boston,
MA, USA}, Yale School of Management, Yale University, New Haven, CT~06520,
USA, April 1989.
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K.~M. Anstreicher.
\newblock The worst--case step in {Karmarkar's} algorithm.
\newblock {\em Mathematics of Operations Research}, 14:294--302, 1989.
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K.~M. Anstreicher.
\newblock Dual ellipsoids and degeneracy in the projective algorithm for linear
programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
1988}, volume 114 of {\em Contemporary Mathematics}, pages 141--149. American
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K.~M. Anstreicher.
\newblock A standard form variant and safeguarded linesearch for the modified
{Karmarkar} algorithm.
\newblock {\em Mathematical Programming}, 47:337--351, 1990.
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K.~M. Anstreicher.
\newblock Advances in interior point methods for linear programming.
\newblock {Tutorial held at the ORSA/TIMS Joint National Meeting in Anaheim,
CA, USA}, Department of Management Science, University of Iowa, Iowa City,
IA~52242, USA, November 1991.
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K.~M. Anstreicher.
\newblock A combined phase\,{I}\,--\,phase\,{II} scaled potential algorithm for
linear programming.
\newblock {\em Mathematical Programming}, 52:429--439, 1991.
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K.~M. Anstreicher.
\newblock On monotonicity in the scaled potential algorithm for linear
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\newblock {\em Linear Algebra and Its Applications}, 152:223--232, 1991.
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K.~M. Anstreicher.
\newblock On the performance of {Karmarkar's} algorithm over a sequence of
iterations.
\newblock {\em SIAM Journal on Optimization}, 1(1):22--29, 1991.
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K.~M. Anstreicher.
\newblock Efficient centering for linear programming interior point methods.
\newblock {Technical Report}, Department of Management Science, University of
Iowa, Iowa City, IA~52242, USA, January 1992.
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K.~M. Anstreicher.
\newblock On interior algorithms for linear programming with no regularity
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\newblock {\em Operations Research Letters}, 11:209--212, 1992.
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K.~M. Anstreicher.
\newblock Strict monotonicity and improved complexity in the standard form
projective algorithm for linear programming.
\newblock {\em Mathematical Programming}, 62:517--535, 1993.
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K.~M. Anstreicher.
\newblock Large step volumetric potential reduction algorithms for linear
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\newblock {\em Annals of Operations Research}, 62:521--538, 1996.
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K.~M. Anstreicher.
\newblock On long step path following and {SUMT} for linear and quadratic
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\newblock {\em SIAM Journal on Optimization}, 6:33--46, 1996.
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K.~M. Anstreicher.
\newblock Potential reduction algorithms.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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Academic Publishers, Dordrecht, The Netherlands, 1996.
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\newblock Ellipsoidal approximations of convex sets based on the volumetric
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\newblock {Technical Report}, Department of Mathematics, University of Iowa,
Iowa City, IA~52242, USA, March 1997.
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\newblock {\em {Interior Point Methods in Theory and Practice}}, volume~76 of
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\newblock North Holland, Amsterdam, The Netherlands, 1997.
\newblock (Special issue).
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\newblock On {Vaidya's} volumetric cutting plane method for convex programming.
\newblock {\em Mathematics of Operations Research}, 22:63--89, 1997.
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K.~M. Anstreicher.
\newblock Volumetric path following algorithms for linear programming.
\newblock {\em Mathematical Programming}, 76:245--263, 1997.
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\newblock On the equivalence of convex programming bounds for {Boolean}
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\newblock {Technical Report}, Department of Mathematics, University of Iowa,
Iowa City, IA~52242, USA, May 1998.
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\newblock The volumetric barrier for convex quadratic constraints.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
Iowa City, IA~52242, USA, October 1998.
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\newblock The volumetric barrier for semidefinite programming.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
Iowa City, IA~52242, USA, January 1998.
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K.~M. Anstreicher.
\newblock Towards a practical volumetric cutting plane method for convex
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\newblock {\em SIAM Journal on Optimization}, 9:190--206, 1999.
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K.~M. Anstreicher and R.~A. Bosch.
\newblock On partial updating in a potential reduction linear programming
algorithm of {Kojima, Mizuno and Yoshise}.
\newblock {Technical Report}, Yale School of Management, Yale University, New
Haven, CT~06520, USA, 1991.
\newblock Same as Bosch and Anstreicher \cite{ipm:Bosch2}.
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K.~M. Anstreicher and R.~A. Bosch.
\newblock Long steps in a ${O(n^{3}L)}$ algorithm for linear programming.
\newblock {\em Mathematical Programming}, 54:251--265, 1992.
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K.~M. Anstreicher and R.~A. Bosch.
\newblock A new infinity--norm path following algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:236--246, 1995.
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K.~M. Anstreicher and M.~Fampa.
\newblock A long--step path following algorithm for semidefinite programming
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\newblock In P.~M. Pardalos and M.~Wolkowicz, editors, {\em Topics in
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\newblock Following a ''balanced'' trajectory from an infeasible point to an
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\newblock {\em Mathematics of Operations Research}, 21:839--859, 1996.
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\newblock {\em {Interior Point Methods in Mathematical Programming}}, volume~62
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\newblock Baltzer Science Publishing Company, Basel, Switzerland, 1996.
\newblock Special issue.
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\newblock {\em Algorithmica}, 10:365--382, 1993.
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\newblock More on dual ellipsoids and degeneracy in interior algorithms for
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, Department of Management Science, University of Iowa, Iowa City,
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\newblock Probabilistic analysis of an infeasible primal--dual algorithm for
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\newblock {Reports on Computational Mathematics}~27, Department of Mathematics,
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\newblock Average performance of a self--dual interior--point algorithm for
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\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
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\newblock Average performance of an ellipsoid termination criterion for linear
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\newblock {Technical Report} 92--01, Department of Management Science,
University of Iowa, Iowa City, IA~52242, USA, February 1992.
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\newblock {\em Optimization Methods and Software}, 3:273--283, 1994.
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\newblock A family of search directions for {Karmarkar's} algorithm.
\newblock {\em Operations Research}, 41:759--767, 1993.
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\newblock On {Lagrangian} relaxation of quadratic matrix constraints.
\newblock {Research Report} CORR 98--24, Department of Combinatorics and
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\newblock {\em Optimization}, 28:149--164, 1993.
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\newblock {\em Mathematical Programming}, 69:45--73, 1995.
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\newblock {\em Proceedings of the American Control Conference (Chicago, IL,
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R.~M. Freund.
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R.~M. Freund.
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R.~M. Freund.
\newblock Theoretical efficiency of a shifted barrier function algorithm for
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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R.~M. Freund.
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R.~M. Freund.
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R.~M. Freund and M.~A. Nunez.
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\newblock {Sloan Working Paper}, Sloan School of Management, Massachusetts
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\newblock Submitted to {\em Mathematical Programming}. Identical version to
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R.~M. Freund and K.~C. Tan.
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R.~M. Freund and K.~C. Tan.
\newblock Newton's method for the general parametric centering problem with
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\newblock {Working Paper}, Sloan School of Management, Massachusetts Institute
of Technology, Cambridge, MA~02139, USA, 1990.
\newblock To appear in {\em Mathematical Programming}.
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R.~M. Freund and K.~C. Tan.
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\newblock {\em Mathematics of Operations Research}, 16(4):775--801, 1991.
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R.~M. Freund and M.~J. Todd.
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\newblock {Sloan Working Paper} 3862--95--MSA, Sloan School of Management,
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\newblock Submitted to {\em Mathematical Programming}.
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\newblock Implementation and empirical study of a combined
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\newblock {Working Paper} 3411--92, Sloan School of Management, Massachusetts
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\newblock {AT \& T Numerical Analysis Manuscript} 94--17, AT{\&}T Bell
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\newblock {Technical Report} ES--230/90, Department of Systems Engineering and
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\newblock {Talk held at the First International Symposium on Interior Point
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\newblock An overview of ${O(\sqrt{n}L)}$--iteration algorithms for linear
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\newblock {Talk held at the 14th Conference on the Mathematics of Operations
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\newblock Polynomial affine algorithms for linear programming.
\newblock {\em Mathematical Programming}, 49:7--21, 1990.
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C.~C. Gonzaga.
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\newblock {\em Mathematical Programming}, 52:209--225, 1991.
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\newblock An interior trust region method for linearly constrained
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\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
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\newblock Large steps path--following methods for linear programming,
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\newblock {\em SIAM Journal on Optimization}, 1:268--279, 1991.
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\newblock Large steps path--following methods for linear programming,
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\newblock {\em SIAM Journal on Optimization}, 1:280--292, 1991.
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\newblock On lower bound updates in primal potential reduction methods for
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\newblock {\em Mathematical Programming}, 52:415--428, 1991.
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\newblock On the convergence of the large step affine--scaling algorithm for
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\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
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\newblock Search directions for interior linear programming methods.
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\newblock {Technical Report}, Department of Mathematical Sciences, Rice
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\newblock (In preparation).
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\newblock {Technical Report} TR~94--48, Department of Mathematical Sciences,
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
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\newblock {Talk held at the 12th Symposium on Mathematical Programming in
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\newblock Integrability of vector and polyvector fields associated with
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\newblock {\em Mathematical Programming}, 52:511--525, 1991.
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\newblock A proof of the polynomiality of the {Iri--Imai} method for linear
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\newblock {\em Journal of Complexity}, 9:269--290, 1993.
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\newblock A multiplicative penalty function for linear programming-- another
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\newblock {\em Proceedings of the 6th Mathematical Programming Symposium of
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\newblock {\em Algorithmica}, 1(4):455--482, 1986.
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\newblock Theory of the multiplicative penalty function method for linear
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\newblock {\em Proceedings of the Institute Statistical Mathematics},
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\newblock (In Japanese).
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\newblock A primal--dual interior--point algorithm for state--constrained {LQ}
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\newblock {\em Proceedings of the 1995 American Control Conference (Seattle,
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\newblock {\em Computational Optimization and Applications}, 4:189--201, 1995.
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\newblock {Manuscript}, School of Industrial and Systems Engineering, Georgia
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\newblock PhD thesis, Department of Operations Research, North Carolina State
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\newblock See Jan \cite{ipm:Jan3}, and Jan and Fang \cite{ipm:Jan2}.
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\newblock A new variant of the primal affine scaling method for linear
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\newblock {\em Optimization}, 22(5):681--715, 1991.
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\newblock {Perspektivy Karmarkarova algorithmu v linearnim programovani
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\newblock {\em Ekonomicko--Matematicky Obzor (Czechoslovakia)}, 25(1):50--63,
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\newblock (In Czech).
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\newblock An introduction to interior point algorithms for linear and convex
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\newblock {Technical Report} 9276/A, Economic Institute, Erasmus University
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\newblock {Technical Report} 92--21, Faculty of Technical Mathematics and
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\newblock New subtitle: {\em Optimal bases versus optimal partitions for
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\newblock {Technical Report} 95--70, Faculty of Technical Mathematics and
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\newblock {Technical Report} 95--45, Faculty of Technical Mathematics and
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\newblock {\em Statistica Nederlandica}, 50:146--170, 1996.
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\newblock In K.~Frauendorfer, H.~Glavitsch, and R.~Bacher, editors, {\em
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\newblock {\em Mathematical Programming}, 76:117--130, 1997.
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\newblock {DFG--Report}~35, Institut f{\"u}r Angewandte Mathematik und
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\newblock DFG--Report~67, Institut f{\"u}r Angewandte Mathematik und Statistik,
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\newblock Revised October 1988. The revised version is identical to Jarre
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\newblock Preprint 165, Institut f{\"u}r Angewandte Mathematik und Statistik,
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\newblock {\em The method of analytic centers for smooth convex programs}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
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\newblock {Talk held at the First International Symposium on Interior Point
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\newblock Interior--point methods for convex programming.
\newblock {Technical Report} SOL~90--16, Systems Optimization Laboratory,
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\newblock On the convergence of the method of analytic centers when applied to
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\newblock {\em Mathematical Programming}, 49:341--358, 1990/91.
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\newblock An efficient line--search for logarithmic barrier functions.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
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\newblock An efficient line search for logarithmic barrier functions.
\newblock {Technical Report} 188, Institut f{\"u}r Angewandte Mathematik und
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\newblock For an extended abstract see Jarre \cite{ipm:Jarre17}.
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\newblock Interior--point methods for convex programming.
\newblock {\em Applied Mathematics \& Optimization}, 26:287--311, 1992.
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\newblock An interior--point method for minimizing the largest eigenvalue of a
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\newblock {\em SIAM Journal on Control and Optimization}, 31:1360--1377, 1993.
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\newblock Interior--point methods via self--concordance or relative {Lipschitz}
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\newblock {Habilitationthesis}, Institut f{\"u}r Angewandte Mathematik und
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\newblock A new line--search step based on the {Weierstrass}
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\newblock {\em Numerische Mathematik}, 68:81--94, 1994.
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\newblock Optimal ellipsoidal approximations around the analytic center.
\newblock {\em Applied Mathematics \& Optimization}, 30:15--19, 1994.
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\newblock Interior--point methods via self--concordance or relative {Lipschitz}
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\newblock {\em Optimization Methods and Software}, 5:75--104, 1995.
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\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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\newblock A {QQP}--minimization method for semidefinite and smooth nonconvex
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\newblock {Technical Report}, Mathematisches Institut der Universit{\"a}t
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F.~Jarre, M.~Kocvara, and J.~Zowe.
\newblock Interior point methods for mechanical design problems.
\newblock {Preprint} 173, Institut f{\"u}r Angewandte Mathematik,
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\newblock Optimal truss design by interior--point methods.
\newblock {\em SIAM Journal on Optimization}, 8:1084--1107, 1998.
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F.~Jarre and S.~Mizuno.
\newblock An infeasible--interior--point algorithm using projections onto a
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\newblock {Technical Report} 206, Institut f{\"u}r Angewandte Mathematik und
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\newblock An adaptive primal--dual method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
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\newblock A practical interior--point method for convex programming.
\newblock {\em SIAM Journal on Optimization}, 5:149--171, 1995.
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\newblock In A.~Bensoussan and J.~L. Lions, editors, {\em Analysis and
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\newblock Extending {Mehrotra's} corrector for linear programs.
\newblock {Preprint} 219, Mathematische Institute der Universit{\"a}t
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\newblock On the role of the objective function in barrier methods.
\newblock {Preprint} MSC--P485--1294, Mathematics and Computer Science
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\newblock {Technical Report}, Mathematical Sciences Department,
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\newblock {\em IBM Journal of Research and Development}, 38:307--321, 1994.
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\newblock A variation of {Karmarkar's} algorithm to solve linear programs in
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
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\newblock On the average complexity of finding an {$\varepsilon$}--optimal
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\newblock {Reports on Computational Mathematics}~25, Department of Mathematics,
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\newblock An interior--point algorithm for quadratically constrained entropy
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\newblock {\em Journal of Optimization Theory and Applications}, 77:79--95,
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\newblock Tapia indicators and finite termination of
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\newblock In J.~Renegar, M.~Shub, and S.~Smale, editors, {\em The Mathematics
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\newblock {\em Journal of Optimization Theory and Applications}, 85:187--199,
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\newblock On the local convergence of a predictor--corrector method for
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\newblock {Reports on Computational Mathematics}~98, Department of Mathematics,
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\newblock {Technical Report} TR--91--23, Department of Mathematical Sciences,
Rice University, Houston, TX~77251, USA, 1991.
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\newblock A predictor--corrector method for solving the
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\newblock {\em Optimization Methods and Software}, 6:109--126, 1995.
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\newblock Complexity analysis of {Karmarkar's} algorithm.
\newblock {Working Paper} 90--5, Department of Mathematics, The University of
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\newblock A complexity analysis for interior--point algorithms based on
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\newblock {\em SIAM Journal on Optimization}, 4:512--520, 1994.
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\newblock A long step primal--dual path--following method for semidefinite
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\newblock {Science Report} 96009, Department of Applied Mathematics, Tsinghue
University, Beijing~100084, China, March 1996.
\newblock To appear in {\em{Operations Research Letters}}.
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\newblock A logarithmic barrier {Newton} method for semidefinite programming.
\newblock {\em Systems Science and Mathematical Sciences}, 10(2):168--175,
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\newblock Predictor--corrector method for extended linear--quadratic
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\newblock {\em Computers and Operations Research}, 23:755--767, 1996.
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\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
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\newblock {Technical Report} 596, Department of Mathematical Sciences,Clemson
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\newblock This is subsumed by Jung et al.\ \cite{ipm:Jung2}.
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\newblock {\em ORSA Journal on Computing}, 6:94--105, 1994.
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\newblock {Technical Report} 597, Department of Mathematical Sciences, Clemson
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\newblock This is subsumed by Jung et al.\ \cite{ipm:Jung2}.
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\newblock {Technical Report} LCSR--TR--91, Laboratory for Computer Science
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\newblock Derivation of a generalized and strenghtened {Gordan Theorem} from
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\newblock {Technical Report} LCSR--TR--121, Laboratory for Computer Science
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\newblock Canonical problems for quadratic programming and projective methods
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\newblock Karmarkar's algorithm with improved steps.
\newblock {\em Mathematical Programming}, 46:73--78, 1990.
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\newblock Generalization of {Karmarkar's} algorithm to convex homogeneous
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\newblock {\em Operations Research Letters}, 11:93--98, 1992.
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\newblock A theorem of the alternative for multihomogeneous functions and its
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\newblock {\em Linear Algebra and Its Applications}, 236:1--24, 1996.
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J.~A. Kaliski.
\newblock {\em A decomposition variant for large scale linear programming}.
\newblock PhD thesis, Department of Management Science, College of Business
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J.~A. Kaliski, D.~Haglin, C.~Roos, and T.~Terlaky.
\newblock Logarithmic barrier decomposition methods for semi--infinite
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\newblock {Technical Report} 96--51, Faculty of Technical Mathematics and
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\newblock To appear in {\em International Transactions in Operations Reseach}.
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\newblock Convergence behavior of {Karmarkar's} projective algorithm for
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\newblock {\em Operations Research Letters}, 10:389--393, 1991.
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J.~A. Kaliski and Y.~Ye.
\newblock A decomposition variant of the potential reduction algorithm for
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\newblock {Working Paper} 91--11, Department of Management Science, College of
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J.~A. Kaliski and Y.~Ye.
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A.~P. Kamath and N.~K. Karmarkar.
\newblock Continuous approach to compute upper bounds in quadratic maximization
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A.~P. Kamath and N.~K. Karmarkar.
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A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
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\newblock In D.~S. Johnson and C.~C. McGeogh, editors, {\em Network Flows and
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\bibitem{ipm:Kamath6}
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\newblock Computational and complexity results for an interior point algorithm
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\newblock {Technical Report} TR--21/93, Dipartimento di Informatica, Universita
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\newblock To appear in {\em Netflow}. See also Kamath et al.
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A.~P. Kamath, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock Computational and complexity results for an interior point algorithm
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\newblock {Technical Report}, Department of Computer Science, Stanford
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\bibitem{ipm:Kamath1}
A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
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\newblock {\em Annals of Operations Research}, 25:43--58, 1990.
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A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
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\newblock {\em Mathematical Programming}, 57:215--238, 1992.
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A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
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\newblock {\em Proceedings of the 36th MSCAS}, pages 185--189, 1993.
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A.~P. Kamath and O.~Palmon.
\newblock Improved interior point algorithms for exact and approximate solution
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\newblock {\em Proceedings of the Sixth Annual ACM--SIAM Symposium on Discrete
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\newblock {\em Integer Programming and Combinatorial Optimization}.
\newblock University of Waterloo Press, Waterloo, Ontario, Canada, 1990.
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\newblock Some tools allowing interior--point methods to become noninterior.
\newblock {Preprint (Hamburger Beitr{\"a}ge zur Angewandten Mathematik)}
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\newblock Proximal methods in view of interior point strategies.
\newblock {\em Journal of Optimization Theory and Applications}, 98:399--429,
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\newblock Fast algorithms for convex quadratic programming and multicommodity
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\newblock {\em Proceedings of the 18th Annual ACM Symposium on Theory of
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\bibitem{ipm:Kapoor2}
S.~Kapoor and P.~M. Vaidya.
\newblock An extension of {Karmarkar's} interior point method to convex
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\newblock {Technical Report}, Department of Computer Science, University of
Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1988.
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\newblock Speeding--up {Karmarkar's} algorithm for multicommodity flows.
\newblock {\em Mathematical Programming}, 73:111--127, 1996.
\newblock A preliminary version is given in Kapoor and Vaidya
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S.~E. Karisch and F.~Rendl.
\newblock Semidefinite programming and graph equipartion.
\newblock {Technical Report} 302--CDLDO~55, Department of Mathematics, Graz
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S.~E. Karisch, F.~Rendl, and J.~Clausen.
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\newblock {Technical Report} DIKU--TR--97/9, Department of Computer Science,
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S.~E. Karisch, F.~Rendl, H.~Wolkowicz, and Q.~Zhao.
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\newblock {Technical Report} CORR\,95--27, Department of Combinatorics and
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\newblock {\em Linear Programming}, chapter 5\,: {Karmarkar's} algorithm, pages
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\newblock Birkh{\"a}user Verlag, Basel, Switzerland, 1991.
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\newblock A new polynomial--time algorithm for linear programming.
\newblock {\em Proceedings of the 16th Annual ACM Symposium on Theory of
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N.~K. Karmarkar.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {\em Combinatorica}, 4:373--395, 1984.
\bibitem{ipm:Karmarkar3}
N.~K. Karmarkar.
\newblock Some comments on the significance of the new polynomial--time
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\newblock {Technical Report}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974,
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\bibitem{ipm:Karmarkar18}
N.~K. Karmarkar.
\newblock Why is the new algorithm better than simplex method and ellipsoid
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\newblock {Extended Abstract}, AT~\&~T~Bell Laboratories, Murray Hill,
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\newblock Recent developments in new approaches to linear programming.
\newblock {Talk held at the SIAM Conference on Optimization, Houston, TX, USA},
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N.~K. Karmarkar.
\newblock An interior--point approach to {NP}--complete problems.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
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N.~K. Karmarkar.
\newblock Methods and apparatus for efficient resource allocation.
\newblock U.S.~Patent No.~4.744.028, 1988.
\newblock AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA.
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\newblock An interior--point approach to {NP}--complete problems -- {Part I}.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\newblock Riemannian geometry underlying interior--point methods for linear
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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N.~K. Karmarkar.
\newblock A new parallel architecture for sparse matrix computation based on
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Proceedings of
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\bibitem{ipm:Karmarkar15}
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\newblock Interior--point methods in optimization.
\newblock In {\em Proceedings of the Second International Conference on
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\bibitem{ipm:Karmarkar14}
N.~K. Karmarkar, J.~C. Lagarias, L.~Slutsman, and P.~Wang.
\newblock Power--series variants of {Karmarkar--type} algorithms.
\newblock {\em AT~\&~T Technical Journal}, 68:20--36, 1989.
\bibitem{ipm:Karmarkar7}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Further developments in the new polynomial--time algorithm for linear
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Boston, MA,
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\bibitem{ipm:Karmarkar8}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Implementation and computational aspects of the {Karmarkar} algorithm
for linear programming, using an iterative method for computing projections.
\newblock {Technical Memorandum}, AT~\&~T Bell Laboratories, Murray Hill,
NJ~07974, USA, 1989.
\newblock See Karmarkar and Ramakrishnan \cite{ipm:Karmarkar9}.
\bibitem{ipm:Karmarkar10}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Robust control system models and their solution by the {Karmarkar}
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\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, AT~\&~T
Bell Laboratories, Murray Hill, NJ~07974, USA, July 1990.
\bibitem{ipm:Karmarkar9}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Computational results of an interior point algorithm for large scale
linear programming.
\newblock {\em Mathematical Programming}, 52:555--586, 1991.
\bibitem{ipm:Karmarkar12}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior point algorithm for zero--one integer programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ 07974, USA, October 1988.
\bibitem{ipm:Karmarkar20}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior--point approach to the maximum independent set problem in
dense random graphs.
\newblock {Manuscript}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA,
1988/1990.
\bibitem{ipm:Karmarkar13}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock Further developments on an interior point algorithm for zero--one
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\newblock {Talk held at the First International Symposium on Interior Point
Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
Netherlands}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, January
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\bibitem{ipm:Karmarkar17}
N.~K. Karmarkar, M.~G.~C. Resende, and K.~G. Ramakrishnan.
\newblock An interior point algorithm to solve computationally difficult set
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\newblock {\em Mathematical Programming}, 52:597--618, 1991.
\bibitem{ipm:Karmarkar11}
N.~K. Karmarkar and L.~P. Sinha.
\newblock Application of {Karmarkar's} algorithm to overseas telecommunications
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\newblock {Talk held at the 12th International Symposium on Mathematical
Programming in Boston, MA, USA}, AT~\&~T Bell Laboratories, Murray Hill,
NJ~07974, USA, August 1985.
\bibitem{ipm:Karmarkar21}
N.~K. Karmarkar and S.~Thakur.
\newblock An interior--point approach to tensor optimization with application
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\newblock {\em Proceedings of Second Integer programming and Combinatorial
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pages 406--420, 1992.
\bibitem{ipm:Karypis2}
G.~Karypis, A.~Gupta, and V.~Kumar.
\newblock A parallel formulation of interior point algorithms.
\newblock In {\em Proceedings Supercomputing\,'94 (Washington, D.C., USA,
November 1994)}, pages 204--213. IEEE Computer Society, New York, NY, USA,
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\bibitem{ipm:Karypis1}
G.~Karypis, A.~Gupta, and V.~Kumar.
\newblock A highly parallel interior point algorithm.
\newblock {\em Proceedings of the 7th SIAM Conference on Parallel Processing
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\bibitem{ipm:Kas1}
P.~Kas, E.~Klafszky, L.~Malyusz, and G.~Izbirak.
\newblock Minimization of {Bregman's} divergence functions, and its relation to
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\newblock {Technical Report}, Department of Building Management and
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\bibitem{ipm:Kaeschel1}
J.~K{\"a}schel.
\newblock Karmarkar--{\"a}hnliche {Verfahren in der Linearen Optimierung
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\newblock {Talk held at the DGOR--Jahrestagung in Stuttgart--Hohenheim,
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J.~K{\"a}schel.
\newblock {'' An efficient algorithm for linear programming '' of V. Ch.
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\newblock {\em Proceedings of the Indian Academy of Sciences, Mathematical
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\newblock See also Venkaiah\,\cite{ipm:Venkaiah1}.
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R.~Katsura, M.~Fukushima, and T.~Ibaraki.
\newblock Interior methods for nonlinear minimum cost network flow problems.
\newblock {\em Journal of the Operations Research Society of Japan},
32:174--179, 1989.
\bibitem{ipm:Kelly1}
T.~K. Kelly and J.~G. Ecker.
\newblock {EPM\,: An} exterior point method for linear programming.
\newblock {Technical Report}, April 1997.
\bibitem{ipm:Kennings1}
A.~A. Kennings, V.~H. Quintana, and A.~Vannelli.
\newblock Constraint matrix ordering for interior point algorithms on hypercube
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\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
Symposium (Manhattan, KS, USA, September 1994)}, 1:187--195, 1994.
\bibitem{ipm:Kennings2}
A.~A. Kennings and A.~Vannelli.
\newblock An efficient interior point approach for {QP} and {LP} models of the
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\newblock {\em Proceedings of the 39th Midwest Symposium on Circuits and
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\bibitem{ipm:Kennington1}
J.~L. Kennington.
\newblock Using {KORBX} for military airlift applications.
\newblock {\em Proceedings of the 28th IEEE Conference on Decision and
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\bibitem{ipm:Keraghel1}
A.~Keraghel.
\newblock {\em Etude adaptive et comparative des prinicipales variantes dans
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\newblock PhD thesis, Laboratoire ARTEMIS (IMAG), Universite Joseph Fourier,
BP~68, F--38402 St.~Martin d'Heres Cedex, France, 1989.
\newblock (In French).
\bibitem{ipm:Khachian1}
L.~G. Khachian and M.~J. Todd.
\newblock On the complexity of approximating the maximal inscribed ellipsoid
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\newblock {Technical Report} 893, School of Operations Research and Industrial
Engineering, College of Engineering, Cornell University, Ithaca,
NY~14853--3801, USA, 1990.
\bibitem{ipm:Kim3}
K.~Kim.
\newblock {\em The effective integration of simplex and interior point
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\newblock PhD thesis, Department of Pure and Applied Mathematics, Washington
State University, Pullman, WA~99164--3113, USA, 1991.
\newblock According to Part\,I see Kim and Nazareth \cite{ipm:Kim1}, for
Part\,II see Kim and Nazareth \cite{ipm:Kim4}.
\bibitem{ipm:Kim1}
K.~Kim and J.~L. Nazareth.
\newblock The decomposition principle and algorithms for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:119--133, 1991.
\bibitem{ipm:Kim2}
K.~Kim and J.~L. Nazareth.
\newblock Implementation of a primal null--space affine scaling method and its
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\newblock {Technical Report} 92--1, Department of Pure and Applied Mathematics,
Washington State University, Pullman, WA~99164--3113, USA, January 1992.
\bibitem{ipm:Kim4}
K.~Kim and J.~L. Nazareth.
\newblock A primal null--space affine scaling method.
\newblock {\em ACM Transactions on Mathematical Software}, 20:373--392, 1994.
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K.~C. Kiwiel.
\newblock Complexity of some cutting plane methods that use analytic centers.
\newblock {\em Mathematical Programming}, 74:47--54, 1996.
\bibitem{ipm:Kiwiel1}
K.~C. Kiwiel.
\newblock Efficiency of the analytic center cutting plane method for convex
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\newblock {\em SIAM Journal on Optimization}, 1996.
\bibitem{ipm:Klebor1}
S.~Klebor.
\newblock Interior point methods for large scale portfolio optimization.
\newblock Master's thesis, Institute of Mathematics, University of
G{\"o}ttingen, G{\"o}ttingen, Germany, 1994.
\bibitem{ipm:Klerk9}
{E. de} Klerk.
\newblock {\em Interior point methods for semidefinite programming}.
\newblock PhD thesis, Faculty of Technical Mathematics and Informatics, TU
Delft, NL--2600~GA~Delft, The Netherlands, 1997.
\bibitem{ipm:Klerk2}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock A nonconvex weighted potential function for polynomial target
follwing methods.
\newblock {Technical Report} 95--127, Faculty of Technical Mathematics and
Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.
\bibitem{ipm:Klerk1}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Semi--definite problems in truss topology optimization.
\newblock {Technical Report} 95--128, Faculty of Technical Mathematics and
Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.
\bibitem{ipm:Klerk3}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Initialization in semidefinite programming via a self--dual
skew--symmetric embedding.
\newblock {\em Opeartions Research Letters}, 20:213--221, 1997.
\bibitem{ipm:Klerk8}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Primal--dual potential reduction methods for semidefinite programming
using affine--scaling directions.
\newblock {Technical Report} 97--29, Faculty of Technical Mathematics and
Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1997.
\bibitem{ipm:Klerk7}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock A short survey on semidefinite programming.
\newblock In W.~K. Klein~Haneveld et~al., editor, {\em {Ten Years LNMB, Ph.d.
Research and Graduate Courses of the Dutch Network of Operations Research}},
volume 122 of {\em CWI Tracts}, pages 323--339. Centrum for Mathematics and
Informatics (CWI), Amsterdam, The Netherlands, 1997.
\bibitem{ipm:Klerk4}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Infeasible start semidefinite programming algorithms via self--dual
embeddings.
\newblock In P.~M. Pardalos and H.~Wolkowicz, editors, {\em Topics in
Semidefinite and Interior--Point Methods}, volume~18 of {\em Fields Institute
Communications Series}, pages 215--236. American Mathematical Society (AMS),
Providence, Rhode Island, USA, 1998.
\bibitem{ipm:Klerk5}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock On primal--dual path following algorithms for semidefinite
programming.
\newblock In F.~Gianessi, S.~Koml{\'o}si, and T.~Rapcs{\'a}k, editors, {\em
{New Trends in Mathematical Programming}}, pages 137--157. Kluwer Academic
Publishers, Dordrecht, The Netherlands, 1998.
\bibitem{ipm:Klerk6}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Polynomial primal--dual affine scaling algorithms in semidefinite
programming.
\newblock {\em Journal of Combinatorial Optimization}, 2:51--69, 1998.
\bibitem{ipm:Kliokys1}
E.~Kliokys, E.~Handschin, and M.~Langer.
\newblock An interior point method for state elimination with current magnitude
measurements and inequality constraints.
\newblock {\em Power Industry Computer Application Conference (Salt Lake City,
UT, USA, 1995)}, pages 385--391, 1995.
\newblock See also Handschin et al. \cite{ipm:Handschin1}.
\bibitem{ipm:Knyazev1}
E.~A. Knyazev.
\newblock The method of centers with adaptation of parameters on the basis of
the steepest descent.
\newblock {\em Issledovaniya po Prikladnoi Matematike (Kazanskii Universitet)},
15:13--24, 1988.
\newblock (In Russian).
\bibitem{ipm:Koenker1}
R.~W. Koenker and B.-J. Park.
\newblock An interior point algorithm for nonlinear quantile regression.
\newblock {\em Journal of Econometrics}, 71:265--283, 1996.
\bibitem{ipm:Kojima1}
M.~Kojima.
\newblock Determining basic variables of optimal solutions in {Karmarkar's new
LP} algorithm.
\newblock {\em Algorithmica}, 1(4):499--515, 1986.
\bibitem{ipm:Kojima30}
M.~Kojima.
\newblock A primitive interior--point algorithm for semidefinite programs in
{Mathematica}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--293, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, December 1994.
\bibitem{ipm:Kojima29}
M.~Kojima.
\newblock Basic lemmas in polynomial--time infeasible--interior--point methods
for linear programs.
\newblock {\em Annals of Operations Research}, 62:1--28, 1996.
\bibitem{ipm:Kojima39}
M.~Kojima.
\newblock Semidefinite programming and interior--point methods.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--314, Department of Mathematical and Computing Sciences, Tokyo
Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, April
1996.
\bibitem{ipm:Kojima22}
M.~Kojima and T.~Ishihara.
\newblock On the {$Big~M$} in the affine scaling algorithm.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--255, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, March 1992.
\bibitem{ipm:Kojima32}
M.~Kojima, S.~Kojima, and S.~Hara.
\newblock Linear algebra for semidefinite programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 1004:1--23,
1997.
\bibitem{ipm:Kojima10}
M.~Kojima, Y.~Kurita, and S.~Mizuno.
\newblock Large--step interior point algorithms for linear complementarity
problems.
\newblock {\em SIAM Journal on Optimization}, 3(2):398--412, 1993.
\bibitem{ipm:Kojima9}
M.~Kojima and N.~Megiddo.
\newblock The relation between the path of centers and {Smale's} regularization
of the linear programming problem.
\newblock {\em Linear Algebra and Its Applications}, 152:135--139, 1991.
\bibitem{ipm:Kojima20}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A primal--dual exterior point algorithm for linear programming.
\newblock {Research Report} RJ~8500, IBM Almaden Research Center, San Jose,
CA~95120--6099, USA, December 1991.
\newblock See also Kojima, Megiddo and Mizuno\,\cite{ipm:Kojima27}.
\bibitem{ipm:Kojima43}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A {Lagrangian} relaxation method for approximating the analytic
center of a polytope.
\newblock {Technical Report}, IBM Almaden Research Center, San Jose,
CA~95120--6099, USA, 1992.
\bibitem{ipm:Kojima11}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A general framework of continuation methods for complementarity
problems.
\newblock {\em Mathematics of Operations Research}, 18:945--963, 1993.
\bibitem{ipm:Kojima27}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A primal--dual infeasible--interior--point algorithm for linear
programming.
\newblock {\em Mathematical Programming}, 61:263--280, 1993.
\newblock See also Kojima, Megiddo and Mizuno\,\cite{ipm:Kojima20}.
\bibitem{ipm:Kojima12}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock Theoretical convergence of large--step--primal--dual interior point
algorithms for linear programming.
\newblock {\em Mathematical Programming}, 59:1--21, 1993.
\bibitem{ipm:Kojima21}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A conjugate direction method for approximating the analytic center of
a polytope.
\newblock {\em Journal of Inequalities and Applications}, 2:181--194, 1998.
\bibitem{ipm:Kojima34}
M.~Kojima, N.~Megiddo, S.~Mizuno, and S.~Shindoh.
\newblock Horizontal and vertical decomposition in interior point methods for
linear programs.
\newblock {Research Report} RJ~9901, IBM Almaden Research Center, San Jose,
CA~95120--6099, USA, 1994.
\bibitem{ipm:Kojima19}
M.~Kojima, N.~Megiddo, S.~Mizuno, and A.~Yoshise.
\newblock An artificial self--dual linear program.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, Department of Information Sciences, Tokyo Institute of Technology,
Oh--Okayama, Meguro--ku, Tokyo~152, Japan, May 1992.
\newblock See Kojima et al.\ \cite{ipm:Kojima14}.
\bibitem{ipm:Kojima17}
M.~Kojima, N.~Megiddo, and T.~Noma.
\newblock Homotopy continuation methods for complementarity problems.
\newblock {Research Report} RJ~6638~(63949), IBM Almaden Research Center, San
Jose, CA~95120--6099, USA, 1989.
\bibitem{ipm:Kojima18}
M.~Kojima, N.~Megiddo, and T.~Noma.
\newblock Homotopy continuation methods for nonlinear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 16(4):754--774, 1991.
\bibitem{ipm:Kojima8}
M.~Kojima, N.~Megiddo, T.~Noma, and A.~Yoshise.
\newblock {\em {A Unified Approach to Interior Point Algorithms for Linear
Complementarity Problems}}, volume 538 of {\em Lecture Notes in Computer
Science}.
\newblock Springer Verlag, Berlin, Germany, 1991.
\bibitem{ipm:Kojima15}
M.~Kojima, N.~Megiddo, T.~Noma, and A.~Yoshise.
\newblock A unified approach to interior point algorithms for linear
complementarity problems\,: {A} summary.
\newblock {\em Operations Research Letters}, 10:247--254, 1991.
\bibitem{ipm:Kojima3}
M.~Kojima, N.~Megiddo, and Y.~Ye.
\newblock An interior point potential reduction algorithm for the linear
complementarity problem.
\newblock {\em Mathematical Programming}, 54:267--279, 1992.
\bibitem{ipm:Kojima13}
M.~Kojima, S.~Mizuno, and T.~Noma.
\newblock A new continuation method for complementarity problems with uniform
{$P$}--functions.
\newblock {\em Mathematical Programming}, 43:107--113, 1989.
\bibitem{ipm:Kojima16}
M.~Kojima, S.~Mizuno, and T.~Noma.
\newblock Limiting behavior of trajectories by a continuation method for
monotone complementarity problems.
\newblock {\em Mathematics of Operations Research}, 15(4):662--675, 1990.
\bibitem{ipm:Kojima24}
M.~Kojima, S.~Mizuno, and M.~J. Todd.
\newblock Infeasible--interior--point primal--dual potential--reduction
algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:52--67, 1995.
\newblock See also Mizuno et al.\ \cite{ipm:Mizuno19}.
\bibitem{ipm:Kojima7}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A polynomial--time algorithm for a class of linear complementarity
problems.
\newblock {\em Mathematical Programming}, 44:1--26, 1989.
\bibitem{ipm:Kojima4}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A primal--dual interior point algorithm for linear programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
Interior Point and Related Methods}, pages 29--47. Springer Verlag, New York,
1989.
\bibitem{ipm:Kojima5}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock Ellipsoids that contain all the solutions of a positive
semi--definite linear complementarity problems.
\newblock {\em Mathematical Programming}, 48:415--435, 1990.
\bibitem{ipm:Kojima6}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock An ${O(\sqrt{n}L)}$ iteration potential reduction algorithm for
linear complementarity problems.
\newblock {\em Mathematical Programming}, 50:331--342, 1991.
\bibitem{ipm:Kojima26}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A convex property of monotone complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--267, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, March 1993.
\bibitem{ipm:Kojima14}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A little theorem of the {$Big-M$} in interior point algorithms.
\newblock {\em Mathematical Programming}, 59:361--375, 1993.
\bibitem{ipm:Kojima23}
M.~Kojima, T.~Noma, and M.~Satoh.
\newblock Potential reduction algorithms for monotone complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--251, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, 1992.
\bibitem{ipm:Kojima25}
M.~Kojima, T.~Noma, and A.~Yoshise.
\newblock Global convergence and detecting infeasibility in interior--point
algorithms.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--257, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, September 1992.
\newblock See also Kojima, Noma and Yoshise \cite{ipm:Kojima28}.
\bibitem{ipm:Kojima28}
M.~Kojima, T.~Noma, and A.~Yoshise.
\newblock Global convergence in infeasible--interior--point algorithms.
\newblock {\em Mathematical Programming}, 65:43--72, 1994.
\newblock See also Kojima, Noma and Yoshise \cite{ipm:Kojima25}.
\bibitem{ipm:Kojima35}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Global and local convergence of predictor--corrector
infeasible--interior--point algorithms for semidefinite programs.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--305, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, October 1995.
\bibitem{ipm:Kojima38}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock A note on the {Nesterov--Todd} and the {Kojima--Shindoh--Hara} search
directions in semidefinite programming.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--313, Department of Mathematical and Computing Sciences, Tokyo
Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, April
1996.
\bibitem{ipm:Kojima37}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock A predictor--corrector interior--point algorithm for the semidefinite
linear complementarity problem using the {Alizadeh--Haeberly--Overton} search
direction.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--311, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, January 1996.
\newblock To appear in {\em{SIAM Journal on Optimization}}.
\bibitem{ipm:Kojima31}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Reduction of monotone linear complementarity problems over cones to
linear programs over cones.
\newblock {\em Acta Mathematica Vietnamica}, 22:147--157, 1997.
\bibitem{ipm:Kojima40}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Search directions in the {SDP} and the monotone {SDLCP}\,:
{Generalization} and inexact computation.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--327, Department of Mathematical and Computing Sciences, Tokyo
Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March
1997.
\bibitem{ipm:Kojima36}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Local convergence of predictor--corrector infeasible--interior--point
algorithms for {SDP}s and {SDLCP}s.
\newblock {\em Mathematical Programming}, 80:129--160, 1998.
\bibitem{ipm:Kojima33}
M.~Kojima, S.~Shindoh, and S.~Hara.
\newblock Interior--point methods for the monotone semidefinite linear
complementarity problem in symmetric matrices.
\newblock {\em SIAM Journal on Optimization}, 7:86--125, 1997.
\bibitem{ipm:Kojima2}
M.~Kojima and K.~Tone.
\newblock An efficient implementation of {Karmarkar's new LP} algorithm.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--180, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, 1986.
\bibitem{ipm:Kojima41}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Cones of matrices and successive convex relaxations of nonconvex
sets.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--338, Department of Mathematical and Computing Sciences, Tokyo
Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March
1998.
\bibitem{ipm:Kojima44}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Discretization and localization in successive convex relaxation
methods for nonconvex quadratic optimization problems.
\newblock {Research Report} B--341, Department of Mathematical and Computing
Sciences, Tokyo Institute of Technology, Oh--Okayama, Meguoro, Tokyo\,152,
Japan, July 1998.
\newblock Also availble as\,: Technical Report COOR\,98--34, Department of
Combinatorics and Optimization, University of Waterloo, Waterloo,
Ontario\,N2L\,3G1, Canada.
\bibitem{ipm:Kojima42}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Monotonicity of primal-dual interior-point algorithms for
semidefinite programming problems.
\newblock {\em Optimization Methods and Software}, 10:275--296, 1998.
\bibitem{ipm:Kolata1}
G.~Kolata.
\newblock A fast way to solve hard problems.
\newblock {\em Science}, 225:1379--1380, September 1984.
\bibitem{ipm:Konno2}
H.~Konno.
\newblock Recent advances in linear programming.
\newblock {\em Journal of the Japan Society of Simulation Technology},
6(1):18--26, March 1987.
\newblock (In Japanese).
\bibitem{ipm:Konno1}
H.~Konno and Y.~Yajima.
\newblock Path--following algorithms for solving nonconvex programming
problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
PA, USA}, Institute of Human and Social Science, Institute of Technology,
2--12--1~Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, October 1990.
\bibitem{ipm:Kortanek1}
K.~O. Kortanek.
\newblock Vector--supercomputer experiments with the linear programming scaling
algorithm.
\newblock {Working Paper Series} 87--2, Department of Management Science,
College of Business Administration, University of Iowa, Iowa City, IA~52240,
USA, 1987.
\newblock See Kortanek and Zhu \cite{ipm:Kortanek13}, too.
\bibitem{ipm:Kortanek2}
K.~O. Kortanek.
\newblock A second order affine scaling algorithm for the geometric programming
dual with logarithmic barrier.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Department
of Management Science, College of Business Administration, University of
Iowa, Iowa City, IA~52240, USA, August 1990.
\newblock See Kortanek and Ho \cite{ipm:Kortanek7}.
\bibitem{ipm:Kortanek13}
K.~O. Kortanek.
\newblock Vector--supercomputer experiments with the primal affine linear
programming scaling algorithm.
\newblock {\em SIAM Journal on Scientific Computations}, 14:279--294, 1993.
\bibitem{ipm:Kortanek10}
K.~O. Kortanek and S.~Huang.
\newblock A simultaneous primal--dual potential reduction algorithm for linear
programming.
\newblock {Working Paper Series} 89--2, Department of Management Science,
College of Business Administration, University of Iowa, Iowa City, IA~52240,
USA, 1989.
\bibitem{ipm:Kortanek11}
K.~O. Kortanek and S.~Huang.
\newblock A note on a potential reduction algorithm with simultaneous
primal/dual updating.
\newblock {\em Operations Research Letters}, 10:501--507, 1992.
\bibitem{ipm:Kortanek9}
K.~O. Kortanek, S.~Huang, and J.~Zhu.
\newblock Central path trajectories and controlled dual perturbations for
geometric programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
USA}, Department of Management Science, College of Business Administration,
University of Iowa, Iowa City, IA~52240, USA, November 1991.
\bibitem{ipm:Kortanek5}
K.~O. Kortanek, D.~N. Leo, and M.~Shi.
\newblock An application of a hybrid algorithm for semi--infinite programming.
\newblock {Talk held at the 12th Symposium on Mathematical Programming,
Cambridge, MA, USA}, Department of Management Science, College of Business
Administration, University of Iowa, Iowa City, IA~52240, USA, 1985.
\bibitem{ipm:Kortanek7}
K.~O. Kortanek and H.~No.
\newblock A second order affine scaling algorithm for the geometric programming
dual with logarithmic barrier.
\newblock {\em Optimization}, 23:303--322, 1992.
\bibitem{ipm:Kortanek6}
K.~O. Kortanek, F.~Potra, and Y.~Ye.
\newblock On some efficient interior point methods for nonlinear convex
programming.
\newblock {\em Linear Algebra and Its Applications}, 152:169--189, 1991.
\bibitem{ipm:Kortanek3}
K.~O. Kortanek and M.~Shi.
\newblock Convergence results and numerical experiments on a linear programming
hybrid algorithm.
\newblock {\em European Journal of Operational Research}, 32:47--61, 1987.
\bibitem{ipm:Kortanek14}
K.~O. Kortanek, X.~J. Xu, and Y.~Ye.
\newblock An infeasible interior--point algorithm for solving primal and dual
geometric programs.
\newblock {\em Mathematical Programming}, 76:155--181, 1997.
\bibitem{ipm:Kortanek4}
K.~O. Kortanek and J.~Zhu.
\newblock New purification algorithms for linear programming.
\newblock {\em Naval Research Logistics Quarterly}, 35:571--583, 1988.
\bibitem{ipm:Kortanek12}
K.~O. Kortanek and J.~Zhu.
\newblock A polynomial barrier algorithm for linearly constrained convex
programming problems.
\newblock {\em Mathematics of Operations Research}, 18(1):116--127, 1993.
\bibitem{ipm:Kortanek8}
K.~O. Kortanek and J.~Zhu.
\newblock Controlling the parameter in the logarithmic barrier term for convex
programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 84:117--143,
1995.
\bibitem{ipm:Korytowski1}
A.~Korytowski.
\newblock Inner search methods for linear programming.
\newblock {\em Zastosowania Matematyki (Warshaw, Poland)}, 20(2):307--327,
1990.
\bibitem{ipm:Korzak1}
J.~Korzak.
\newblock {\em {Primal--duale pfadfolgende inexacte
{\"a}u{\ss}ere--Punkte--Verfahren zur L{\"o}sung lineare Optimierungsaufgaben
(Primal--dual path--following inexact exterior point methods for the solution
of linear optimization problems}}.
\newblock PhD thesis, Department of Mathematics and Informatics, University of
Wuppertal, Gauss--Str.20, D--42097 Wuppertal, Germany, 1997.
\newblock (In German).
\bibitem{ipm:Kovacevic1}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Improving the rate of convergence of interior point methods for
linear programming.
\newblock {\em Mathematical Programming}, 52:467--479, 1991.
\bibitem{ipm:Kovacevic2}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Interior point methods for transportation problems.
\newblock {Talk held at the Symposium on Mathematical Programming in
Oberwolfach, Germany}, University of Belgrade, Belgrade, Yugoslavia, January
1992.
\bibitem{ipm:Kovacevic3}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock Stabilization of path--following interior point methods for linear
programming.
\newblock In {\em IX Conference on Applied Mathematics (Budva, 1994)}, pages
245--258. University of Novi Sad, Novi Sad, Yugoslavia, 1995.
\bibitem{ipm:Kovacevic4}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}}.
\newblock A view of interior point methods for linear programming.
\newblock {\em Yugoslavian Journal of Operations Research}, 5:173--193, 1995.
\bibitem{ipm:Kovacevic5}
V.~V. {Kova\u{c}evi{\'c}--Vuj\u{c}i{\'c}} and M.~D. Asi{\'c}.
\newblock An interior point method for transportation problems.
\newblock {\em Facta Universitatis\,: Series Mathematics and Informatics},
11:157--170, 1996.
\bibitem{ipm:Kozlov1}
A.~Kozlov.
\newblock The {Karmarkar} algorithm\,: {Is} it for real~?
\newblock {\em SIAM News}, 18(6):1, 4, 13, November 1985.
\bibitem{ipm:Kozlov2}
A.~Kozlov and L.~W. Black.
\newblock Berkeley obtains new results with {Karmarkar} algorithm.
\newblock {\em SIAM News}, 19(3):3, 20, May 1986.
\bibitem{ipm:Kranich1}
E.~Kranich.
\newblock Interior point methods for mathematical programming\,: {A}
bibliography.
\newblock {Discussion Paper} 171, Institute of Economy and Operations Research,
FernUniversit{\"a}t Hagen, P.O. Box~940, D--5800~Hagen~1, Germany, May 1991.
\newblock Available through {\em netlib}, see Kranich \cite{ipm:Kranich2}.
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\newblock Implementation of affine scaling methods\,: {Towards} faster
implementations with complete {Cholesky} factor in use.
\newblock {Technical Report} 89--15, Department of Industrial Engineering and
Management Science, Northwestern University, Evanston, IL~60208, USA, October
1989.
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S.~Mehrotra.
\newblock On implementation of interior point methods for linear programming\,:
{Karmarkar's} preconditioners.
\newblock {Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver,
British Columbia, Canada}, Department of Industrial Engineering and
Management Science, Northwestern University, Evanston, IL~60208, USA, May
1989.
\bibitem{ipm:Mehrotra20}
S.~Mehrotra.
\newblock Higher order methods and their performance.
\newblock {Technical Report} TR~90--16R1, Department of Industrial Engineering
and Management Science, Northwestern University, Evanston, IL~60208, USA,
1990.
\newblock Revised July 1991.
\bibitem{ipm:Mehrotra9}
S.~Mehrotra.
\newblock Implementations of affine scaling methods\,: {Speeding} up the
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
USA}, Department of Industrial Engineering and Management Science,
Northwestern University, Evanston, IL~60208, USA, May 1990.
\bibitem{ipm:Mehrotra8}
S.~Mehrotra.
\newblock On an implementation of the primal--dual predictor--corrector
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\newblock {Talk held at the Second Asilomar Workshop on Progress in
Mathematical Programming, Asilomar, CA, USA}, Department of Industrial
Engineering and Management Science, Northwestern University, Evanston,
IL~60208, USA, February 1990.
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S.~Mehrotra.
\newblock Finite termination and superlinear convergence in primal--dual
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\newblock {Technical Report} 91--13, Department of Industrial Engineering and
Management Science, Northwestern University, Evanston, IL~60208, USA, July
1991.
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S.~Mehrotra.
\newblock Generalized prediction--corrector methods for solving linear
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
Tennessee, USA}, Department of Industrial Engineering and Management Science,
Northwestern University, Evanston, IL~60208, USA, May 1991.
\bibitem{ipm:Mehrotra18}
S.~Mehrotra.
\newblock Handling free variables in interior methods.
\newblock {Technical Report} 91--06, Department of Industrial Engineering and
Management Science, Northwestern University, Evanston, IL~60208, USA, March
1991.
\bibitem{ipm:Mehrotra17}
S.~Mehrotra.
\newblock Higher--order methods for solving linear programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
Tennessee, USA}, Department of Industrial Engineering and Management Science,
Northwestern University, Evanston, IL~60208, USA, May 1991.
\bibitem{ipm:Mehrotra7}
S.~Mehrotra.
\newblock On finding a vertex solution using interior point methods.
\newblock {\em Linear Algebra and Its Applications}, 152:233--253, 1991.
\bibitem{ipm:Mehrotra22}
S.~Mehrotra.
\newblock Deferred rank--one updates in ${O(n^{3}L)}$ interior point algorithm.
\newblock {\em Journal of the Operations Research Society of Japan},
35:345--352, 1992.
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S.~Mehrotra.
\newblock Finite termination in interior--point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, Department of Industrial Engineering and Management Sciences,
Northwestern University, Evanston, IL~60208, USA, May 1992.
\bibitem{ipm:Mehrotra5}
S.~Mehrotra.
\newblock Implementation of affine scaling methods\,: {Approximate} solutions
of systems of linear equations using preconditioned conjugate gradient
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\newblock {\em ORSA Journal on Computing}, 4:103--118, 1992.
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S.~Mehrotra.
\newblock On the implementation of a primal--dual interior point method.
\newblock {\em SIAM Journal on Optimization}, 2(4):575--601, 1992.
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S.~Mehrotra.
\newblock Quadratic convergence in a primal--dual method.
\newblock {\em Mathematics of Operations Research}, 18:741--751, 1993.
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S.~Mehrotra.
\newblock Asymptotic convergence in a generalized predictor--corrector method.
\newblock {\em Mathematical Programming}, 74:11--28, 1996.
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S.~Mehrotra and R.~Fourer.
\newblock Solving symmetric indefinite systems in interior point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, Department of Industrial Engineering and Management Sciences,
Northwestern University, Evanston, IL~60208, USA, May 1992.
\bibitem{ipm:Mehrotra26}
S.~Mehrotra and R.~D.~C. Monteiro.
\newblock Parametric and range analysis for interior point methods.
\newblock {Technical Report}, Department of Systems and Industrial Engineering,
University of Arizona, Tucson, AZ~85721, USA, April 1992.
\bibitem{ipm:Mehrotra29}
S.~Mehrotra and R.~A. Stubbs.
\newblock Predictor--corrector methods for a class of linear complementarity
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\newblock {\em SIAM Journal on Optimization}, 4:441--453, 1994.
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S.~Mehrotra and J.~Sun.
\newblock An algorithm for convex quadratic programming that requires
${O(n^{3.5}L)}$ arithmetic operations.
\newblock {\em Mathematics of Operations Research}, 15:342--363, 1990.
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S.~Mehrotra and J.~Sun.
\newblock An interior point algorithm for solving smooth convex programs based
on {Newton's} method.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
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S.~Mehrotra and J.~Sun.
\newblock Path--following methods for convex programming.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
Department of Industrial Engineering and Management Science, Northwestern
University, Evanston, IL~60208, USA, July 1990.
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S.~Mehrotra and J.~Sun.
\newblock A method of analytic centers for quadratically constrained convex
quadratic programs.
\newblock {\em SIAM Journal on Numerical Analysis}, 28(2):529--544, 1991.
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S.~Mehrotra and J.~Sun.
\newblock On computing the center of a quadratically constrained set.
\newblock {\em Mathematical Programming}, 50:81--89, 1991.
\bibitem{ipm:Mehrotra10}
S.~Mehrotra and J.~Sun.
\newblock On the implementation of a (primal--dual) interior point method.
\newblock {\em SIAM Journal on Optimization}, 2(4):575--601, 1992.
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S.~Mehrotra and J.-S. Wang.
\newblock Conjugate gradient based implementation of interior point methods for
network flow problems.
\newblock In L.~Adams and J.~L. Nazareth, editors, {\em Linear and Nonlinear
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Summer Research Conference, Seattle, WA, USA, July 9--13, 1995)}, pages
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\newblock On finding the optimal facet of linear programs.
\newblock {Technical Report} TR~91--10, Department of Industrial Engineering
and Management Sciences, Northwestern University, Evanston, IL~60208, USA,
1991.
\newblock See also Mehrotra and Ye\,\cite{ipm:Mehrotra28}.
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\newblock Finding an interior point in the optimal face of linear programs.
\newblock {\em Mathematical Programming}, 62:497--515, 1993.
\newblock See also Mehrotra and Ye\,\cite{ipm:Mehrotra21}.
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\newblock Least absolute value regression.
\newblock {Working Paper}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974,
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M.~S. Meketon.
\newblock Optimization in simulation\,: {A} survey of recent results.
\newblock In A.~Thesen, H.~Grant, and W.~D. Kelton, editors, {\em Proceedings
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\newblock Degeneracy issues in the affine scaling algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
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{J. C. O.} Mello, A.~C.~G. Melo, and S.~Granville.
\newblock Simultaneous transfer capability assessment by combining interior
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\newblock {\em IEEE Transaction on Power Systems}, 12:736--742, 1997.
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\newblock A new linesearch method for quadratically constrained convex
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\newblock {\em Operations Research Letters}, 16:67--77, 1994.
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\newblock A linesearch procedure in barrier methods for some convex programming
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\newblock {\em SIAM Journal on Optimization}, 6:283--298, 1996.
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\newblock Newton modified barrier function complexity for quadratic programming
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\newblock The {Newton} modified barrier method for {QP} problems.
\newblock {\em Annals of Operations Research}, 62:465--519, 1996.
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\newblock {Primal--duale pfadorientierte Innere--{\"A}u{\ss}ere--Punkte--%
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path--following interior--exterior--point methods for solving linear
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\newblock {Habilitationthesis}, Fachbereich Mathematik, Bergische
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\newblock (In German).
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\newblock Implementation of a first order central path following algorithm for
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\newblock {Technical Report} 202, Institut f{\"u}r Angewandte Mathematik und
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\newblock {\em Mise en oeuvre et developpements de la methode de plans coupants
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\newblock PhD thesis, Department of Management Studies, University of Geneva,
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\newblock (In French).
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\newblock {LMIs}, interior point methods, complexity theory, and robust
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\newblock {\em Proceedings of the 35th IEEE conference on Decision and
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\newblock On the modifications of the affine scaling algorithm for linear
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\newblock {\em Alkamazott Matematikai Lapok}, 17:185--194, 1993.
\newblock (In Hungarian, English summary).
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C.~M{\'e}sz{\'a}ros.
\newblock The {''inexact''} minimum local fill--in ordering algorithm.
\newblock {Working Paper} WP 95--7, Computer and Automation Research Institute,
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\newblock Submitted to {\em{ACM Transactions on Mathematical Software}}.
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C.~M{\'e}sz{\'a}ros.
\newblock {\em The efficient implementation of interior point methods for
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\newblock PhD thesis, E{\"o}tv{\"o}s Lor{\'a}nd University of Sciences,
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C.~M{\'e}sz{\'a}ros.
\newblock Fast {Cholesky} factorization of interior point methods of linear
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\newblock {\em Computers and Mathematics with Applications}, 31:49--54, 1996.
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\newblock The augmented system variant of {IPM}s in two--stage stochastic
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\newblock {\em European Journal of Operational Research}, 101:317--327, 1997.
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\newblock Steplengths in infeasible primal--dual interior point algorithms for
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\newblock {Technical Report} DOC~97/7, Imperial College, London, United
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\newblock On aproperty of the {Cholesky} factorization and its consequences in
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\newblock {Working Paper} WP\,98--7, Laboratory of Operations Research and
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\newblock On free variables in interior point methods.
\newblock {\em Optimization Methods and Software}, 9:121--139, 1998.
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\newblock On the sparsity issues of interior point methods for quadratic
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\newblock {Working Paper} WP\,98--4, Laboratory of Operations Research and
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C.~M{\'e}sz{\'a}ros.
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\newblock {Working Paper} WP\,98--3, Laboratory of Operations Research and
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\bibitem{ipm:Meyer1}
R.~R. Meyer and G.~L. Schultz.
\newblock Structured interior point methods for multicommodity flows.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
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\bibitem{ipm:Miagen1}
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\newblock Implementation and numerical experiments on an interior--point
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\newblock In {\em Proceedings of the InfoJapan~'90\ : Information Technology
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\bibitem{ipm:Miao2}
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\newblock A quadratically convergent {$O((1 + \kappa)\sqrt{n}L)$}-- iteration
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\newblock {Research Report} RRR~93--93, RUTCOR\,--\,Rutgers Center for
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\newblock Two infeasible interior--point predictor--corrector algorithms for
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\newblock {\em SIAM Journal on OPtimization}, 6:587--599, 1996.
\bibitem{ipm:Minoux1}
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\newblock New suggested implementation of {Karmarkar's} algorithm.
\newblock Cahier~71, Laboratoire de Analyse et Modelisation de Systemes pour
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\bibitem{ipm:Minoux3}
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\newblock Towards a probabilistic analysis of {Karmarkar's} algorithm.
\newblock Cahier, Laboratoire de Analyse et Modelisation de Systemes pour
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\bibitem{ipm:Minoux2}
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\newblock Probabilistic bounds on one step objective/potential function
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\newblock {\em R.A.I.R.O Recherche Operationnelle/Operations Research},
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\bibitem{ipm:Mitchell1}
J.~E. Mitchell.
\newblock {\em Karmarkar's algorithm and combinatorial optimization problems}.
\newblock PhD thesis, School of Operations Research and Industrial Engineering,
Cornell University, Ithaca, NY~14853--7501, USA, 1988.
\bibitem{ipm:Mitchell13}
J.~E. Mitchell.
\newblock An interior point column generation method for linear programming
using shifted barriers.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
USA}, Rensselaer Polytechnic Institute, Department of Mathematical Sciences,
Troy, NY~12180--3590, USA, November 1991.
\bibitem{ipm:Mitchell11}
J.~E. Mitchell.
\newblock Updating lower bounds when using {Karmarkar's} projective algorithm
for linear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 78:127--142,
1993.
\bibitem{ipm:Mitchell8}
J.~E. Mitchell.
\newblock An interior point column generation method for linear programming
using shifted barriers.
\newblock {\em SIAM Journal on Optimization}, 4:423--440, 1994.
\bibitem{ipm:Mitchell19}
J.~E. Mitchell.
\newblock Interior point methods for combinatorial optimization.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
Programming}, volume~5 of {\em Applied Optimization}, pages 417--466. Kluwer
Academic Publishers, Dordrecht, The Netherlands, 1996.
\newblock See also Mitchell, Pardalos and Resende\,\cite{ipm:Mitchell23}.
\bibitem{ipm:Mitchell16}
J.~E. Mitchell.
\newblock Interior point methods for integer programming.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
Applications}, pages 223--248. Oxford Science Publications, Oxford University
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\bibitem{ipm:Mitchell20}
J.~E. Mitchell.
\newblock Computational experience with an interior point cutting plane
algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
Polytechnic Institute, Troy, NY~12180--3590, USA, February 1997.
\newblock Revised April 1997.
\bibitem{ipm:Mitchell18}
J.~E. Mitchell.
\newblock Fixing variables and generating classical cutting planes when using
an interior branch and cut method to solve integer programming problems.
\newblock {\em European Journal of Operational Research}, 97:139--148, 1997.
\bibitem{ipm:Mitchell21}
J.~E. Mitchell.
\newblock An interior point cutting plane algorithm for {Ising}spin glass
problems.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
Polytechnic Institute, Troy, NY~12180--3590, USA, July 1997.
\newblock Revised April 1997.
\bibitem{ipm:Mitchell14}
J.~E. Mitchell and B.~Borchers.
\newblock A primal--dual interior point cutting plane method for the linear
ordering problem.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
Bulletin}, 21:13--18, 1992.
\bibitem{ipm:Mitchell15}
J.~E. Mitchell and B.~Borchers.
\newblock Solving real--world linear ordering problems using a primal--dual
interior point cutting plane method.
\newblock {\em Annals of Operatiomns Research}, 62:253--276, 1996.
\bibitem{ipm:Mitchell22}
J.~E. Mitchell and B.~Borchers.
\newblock Solving linear ordering problems with a combined interior
point/simplex cutting plane algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
Polytechnic Institute, Troy, NY~12180--3590, USA, September 1997.
\bibitem{ipm:Mitchell23}
J.~E. Mitchell, P.~M. Pardalos, and M.~G.~C. Resende.
\newblock Interior point methods for combinatorial optimization.
\newblock In D.-Z. Du and P.~M. Pardalos, editors, {\em Handbook of
Combinatorial Optimization}, pages 189--298. Kluwer Academic Publishers,
Dordrecht, The Netherlands, 1998.
\newblock See also Mitchell\,\cite{ipm:Mitchell19}.
\bibitem{ipm:Mitchell17}
J.~E. Mitchell and S.~Ramaswamy.
\newblock A long--step, cutting plane algorithm for linear and convex
programming.
\newblock {Technical Report} 37--93--387, Department of Mathematical Sciences,
Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, August 1993.
\newblock Title before August 1994 revision\,: {An extension of Atkinson and
Vaidya's algorithm that uses central trajectory}.
\bibitem{ipm:Mitchell12}
J.~E. Mitchell and M.~J. Todd.
\newblock Two variants of {Karmarkar's} linear programming algorithm for
problems with some unrestricted variables.
\newblock {Technical Report} 741, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--7501, USA, 1987.
\newblock Incorporated in Mitchell and Todd \cite{ipm:Mitchell4}.
\bibitem{ipm:Mitchell3}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving linear ordering problems using {Karmarkar's} algorithm.
\newblock {Technical Report}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--7501, USA, 1988.
\newblock Incorrect citation, elsewhere; part of Mitchell \cite{ipm:Mitchell1},
and of Mitchell and Todd \cite{ipm:Mitchell6}.
\bibitem{ipm:Mitchell2}
J.~E. Mitchell and M.~J. Todd.
\newblock On the relationship between the search directions in the affine and
projective variants of {Karmarkar's} linear programming algorithm.
\newblock In B.~Cornet and H.~Tulkens, editors, {\em Contributions to
Operations Research and Economics\,: The Twentieth Anniversary of CORE},
pages 237--250. M.I.T. Press, Cambridge, MA, USA, 1989.
\bibitem{ipm:Mitchell5}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
algorithm, {Part\,I\,: Theory}.
\newblock {RPI Technical Report} 172, Department of Mathematical Sciences,
Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, January 1989.
\bibitem{ipm:Mitchell6}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
algorithm, {Part\,II\,: Computational} results.
\newblock {RPI Technical Report} 173, Department of Mathematical Sciences,
Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, January 1989.
\bibitem{ipm:Mitchell7}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving perfect matching problems using {Karmarkar's} algorithm.
\newblock {RPI Technical Report} 174, Department of Mathematical Sciences,
Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, August 1989.
\newblock See Mitchell and Todd \cite{ipm:Mitchell10}, too.
\bibitem{ipm:Mitchell4}
J.~E. Mitchell and M.~J. Todd.
\newblock A variant of {Karmarkar's} linear programming algorithm for problems
with some unrestricted variables.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 10:30--38,
1989.
\bibitem{ipm:Mitchell10}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving perfect matching problems using {Karmarkar's} algorithm.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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Mathematical Society, Providence, Rhode Island, USA, 1990.
\bibitem{ipm:Mitchell9}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
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\newblock {\em Mathematical Programming}, 56:245--284, 1992.
\newblock Combination and shortening of Mitchell and Todd
\cite{ipm:Mitchell5,ipm:Mitchell6}.
\bibitem{ipm:Mitra3}
G.~Mitra and R.~Levkovitz.
\newblock {\em {Interior Point Methods for Linear Programming Optimization\,:
Theory and Practice}}.
\newblock John Wiley\,\&\,Sons, New York, USA, 1997.
\bibitem{ipm:Mitra2}
G.~Mitra, M.~Tamiz, and J.~Yadegar.
\newblock Experimental investigation of an interior search method within a
simplex framework.
\newblock {\em Communications of the ACM}, 31(12):1474--1482, 1988.
\bibitem{ipm:Mitra1}
G.~Mitra, M.~Tamiz, and J.~Yadegar.
\newblock A hybrid algorithm for linear programming.
\newblock In A.~J. Osiadacz, editor, {\em Simulation and Optimization of Large
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\newblock An ${O(n^{3}L)}$ algorithm using a sequence for linear
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\newblock {\em Journal of the Operations Research Society of Japan}, 33:66--75,
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\bibitem{ipm:Mizuno2}
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\newblock A rank--one updating interior algorithm for linear programming.
\newblock {\em Arabian Journal for Science and Engineering}, 15(4):671--677,
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\newblock {$O(n^{\rho}L)$} iteration {$O(n^{3}L)$} potential reduction
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\newblock {\em Linear Algebra and Its Applications}, 152:155--168, 1991.
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S.~Mizuno.
\newblock A new polynomial time method for a linear complementarity problem.
\newblock {\em Mathematical Programming}, 56:31--43, 1992.
\bibitem{ipm:Mizuno16}
S.~Mizuno.
\newblock Polynomiality of the {Kojima--Megiddo--Mizuno} infeasible interior
point algorithm for linear programming.
\newblock {Technical Report} 1006, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, May 1992.
\newblock See also Mizuno \cite{ipm:Mizuno21}.
\bibitem{ipm:Mizuno17}
S.~Mizuno.
\newblock A primal--dual interior point method for linear programming.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
Research} B--252, Department of Information Sciences, Tokyo Institute of
Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, January 1992.
\newblock (In Japanese).
\bibitem{ipm:Mizuno21}
S.~Mizuno.
\newblock Polynomiality of infeasible interior--point algorithms for linear
programming.
\newblock {\em Mathematical Programming}, 67:109--119, 1994.
\newblock See also Mizuno \cite{ipm:Mizuno16}.
\bibitem{ipm:Mizuno22}
S.~Mizuno.
\newblock A predictor--corrector infeasible--interior--point algorithm for
linear programming.
\newblock {\em Operations Research Letters}, 16:61--66, 1994.
\bibitem{ipm:Mizuno24}
S.~Mizuno.
\newblock Research in interior--point methods.
\newblock {\em Proceedings of the Institute of Statistical Mathematics (Tokyo,
Japan)}, 42:103--109, 1994.
\newblock (In Japanese).
\bibitem{ipm:Mizuno27}
S.~Mizuno.
\newblock Infeasible--interior--point algorithms.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
Programming}, volume~5 of {\em Applied Optimization}, pages 159--187. Kluer
Academic Publishers, Dordrecht, The Netherlands, 1996.
\bibitem{ipm:Mizuno25}
S.~Mizuno.
\newblock A superlinearly convergent infeasible--interior--point algorithm for
geometrical {LCPs} without a strictly complementarity condition.
\newblock {\em Mathematics of Operations Research}, 21:382--400, 1996.
\bibitem{ipm:Mizuno23}
S.~Mizuno and F.~Jarre.
\newblock An infeasible--interior--point algorithm using projections onto a
convex set.
\newblock {\em Annals of Operations Research}, 62:59--80, 1993.
\newblock See also Mizuno and Jarre \cite{ipm:Jarre18}.
\bibitem{ipm:Mizuno29}
S.~Mizuno and F.~Jarre.
\newblock Global and polynomial--time convergence of an
infeasible--interior--point algorithm using inexact computation.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 981:22--35,
1997.
\newblock See also Mizuno and Jarre\,\cite{ipm:Mizuno31}.
\bibitem{ipm:Mizuno31}
S.~Mizuno and F.~Jarre.
\newblock Global and polynomial--time convergence of an
infeasible--interior--point algorithm using inexact computation.
\newblock {\em Mathematical Programming}, 84:39--53, 1999.
\newblock See also Mizuno and Jarre\,\cite{ipm:Mizuno29}.
\bibitem{ipm:Mizuno26}
S.~Mizuno, F.~Jarre, and J.~Stoer.
\newblock A unified approach to infeasible--interior--point algorithms via
geometrical linear complementarity problems.
\newblock {\em Applied Mathematics\,\&\,Optimization}, 33:315--341, 1996.
\bibitem{ipm:Mizuno19}
S.~Mizuno, M.~Kojima, and M.~J. Todd.
\newblock Infeasible--interior--point primal--dual potential--reduction
algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:52--67, 1995.
\bibitem{ipm:Mizuno3}
S.~Mizuno and K.~Masuzawa.
\newblock Polynomial time interior point algorithms for transportation
problems.
\newblock {\em Journal of the Operations Research Society of Japan},
32:371--382, 1989.
\bibitem{ipm:Mizuno28}
S.~Mizuno, N.~Megiddo, and T.~Tsuchiya.
\newblock A linear programming instance with many crossover events.
\newblock {\em Journal of Complexity}, 12:474--479, 1996.
\bibitem{ipm:Mizuno14}
S.~Mizuno and A.~Nagasawa.
\newblock Strict monotonicity in {Todd's} low--complexity algorithm for linear
programming.
\newblock {\em Operations Research Letters}, 12:59--64, 1992.
\bibitem{ipm:Mizuno15}
S.~Mizuno and A.~Nagasawa.
\newblock A primal--dual affine scaling potential reduction algorithm for
linear programming.
\newblock {\em Mathematical Programming}, 62:119--131, 1993.
\bibitem{ipm:Mizuno13}
S.~Mizuno, R.~Saigal, and J.~B. Orlin.
\newblock Determination of optimal vertices from feasible solution in
unimodular programming.
\newblock {\em Mathematical Programming}, 59:23--31, 1993.
\bibitem{ipm:Mizuno11}
S.~Mizuno and M.~J. Todd.
\newblock An {$O(n^{3}L)$} long step path following algorithm for a linear
complementarity problem.
\newblock {Technical Report}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1989.
\newblock Same as Mizuno and Todd \cite{ipm:Mizuno12}.
\bibitem{ipm:Mizuno12}
S.~Mizuno and M.~J. Todd.
\newblock An {$O(n^{3}L)$} adaptive path following algorithm for a linear
complementarity problem.
\newblock {\em Mathematical Programming}, 52:587--595, 1991.
\bibitem{ipm:Mizuno30}
S.~Mizuno and M.~J. Todd.
\newblock On two homogeneous self--dual systems for linear programming and its
extensions.
\newblock {Research Memorandum} 687, The Institute of Statistical Mathematics,
4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, 1998.
\newblock Also issued as {Technical Report No.\,1213, School of Operations
Research and Industrial Engineering, Cornell University, Ithaca,
NY~14853--3801, USA}.
\bibitem{ipm:Mizuno18}
S.~Mizuno, M.~J. Todd, and L.~Tun{\c c}el.
\newblock Monotonicity of primal and dual objective values in primal--dual
interior--point algorithms.
\newblock {\em SIAM Journal on Optimization}, 4:613--625, 1994.
\bibitem{ipm:Mizuno4}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of path--following algorithms for linear
programming.
\newblock {Technical Report} 878, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1989.
\newblock See Mizuno et al.\ \cite{ipm:Mizuno8}.
\bibitem{ipm:Mizuno6}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of interior point algorithms for linear
programming.
\newblock {Technical Report}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1990.
\newblock Incorrect citation, elsewhere.
\bibitem{ipm:Mizuno5}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of long--step algorithms for linear programming.
\newblock {Technical Report} 882, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1990.
\newblock Also available as {\em Technical Report 24, Department of Management
Science and Engineering, Tokyo Institute of Technology, Oh--Okayama,
Meguro--ku, Tokyo~152, Japan, 1989} and {\em Technical Report 89--23,
Department of Management Science, University of Iowa, Iowa City, IA~52242,
USA, 1989}. See also Mizuno et al.\, \cite{ipm:Mizuno8}.
\bibitem{ipm:Mizuno8}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock On adaptive--step primal--dual interior--point algorithms for linear
programming.
\newblock {\em Mathematics of Operations Research}, 18:964--981, 1993.
\newblock Revised and combined version of Mizuno et al.\,
\cite{ipm:Mizuno4,ipm:Mizuno5}.
\bibitem{ipm:Mizuno20}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock A surface of analytic centers and infeasible--interior--point
algorithms for linear programming.
\newblock {\em Mathematics of Operations Research}, 20:135--162, 1995.
\bibitem{ipm:Mizuno7}
S.~Mizuno, A.~Yoshise, and T.~Kikuchi.
\newblock Practical polynomial time algorithms for linear complementarity
problems.
\newblock {\em Journal of the Operations Research Society of Japan}, 32:75--92,
1989.
\bibitem{ipm:Momoh7}
J.~A. Momoh, R.~F. Austin, R.~Adapa, and E.~C. Ogbuobiri.
\newblock Application of interior point method to economic dispatch.
\newblock {\em Proceedings of the IEEE International Conference on Systems, Man
and Cybernetics (Chicago, IL, USA, October 1992)}, 2:1096--1101, 1993.
\bibitem{ipm:Momoh4}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock Evaluation of interior point methods and their application to power
systems economic dispatch.
\newblock {\em Proceedings of the 1993 North American Power Symposium
(Washington, D.C., USA, October 1993)}, pages 116--123, 1994.
\bibitem{ipm:Momoh2}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock Rule based support for partioning networks for optimal power flows.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
Symposium (Manhattan, KS, USA, September 1994)}, 1:376--381, 1994.
\bibitem{ipm:Momoh5}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock {VAr} planning using partitioned power system networks.
\newblock {\em Proceedings of the 36th Midwest Symposium on Circuits and
Systems (Detroit, MI, USA, August 1993)}, 1:372--376, 1994.
\bibitem{ipm:Momoh3}
J.~A. Momoh and S.~X. Guo.
\newblock An enhanced quadratic interior point method to solve power system
{VAr} planning.
\newblock {\em Proceedings of the 1993 North American Power Symposium
(Washington, D.C., USA, October 1993)}, pages 215--221, 1994.
\bibitem{ipm:Momoh1}
J.~A. Momoh, S.~X. Guo, E.~C. Ogbuobiri, and R.~Adapa.
\newblock The quadratic interior point method solving power system optimization
problems.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:1327--1336, 1994.
\newblock See also\,: {\em IEEE International Conference on Systems, Man and
Cybernetics 1\,(1992), 1096--}.
\bibitem{ipm:Momoh6}
J.~A. Momoh, P.~J. Lusaka, R.~Adapa, and E.~C. Ogbuobiri.
\newblock Heurstic--based algorithms for enhanced interior point based {OPF}.
\newblock {\em Expert System Application to Power Systems (Proceedings of the
January 1993 Melbourne Conference)}, IV:686--696, 1994.
\bibitem{ipm:Monma1}
C.~L. Monma.
\newblock Recent breakthroughs in linear programming methods.
\newblock {Internal Memorandum}, Bell Communications Research, Morristown,
NJ~07960, USA, 1987.
\bibitem{ipm:Monma2}
C.~L. Monma.
\newblock Successful implementations of interior algorithms.
\newblock {\em SIAM News}, 22(2):14--16, March 1989.
\bibitem{ipm:Monma3}
C.~L. Monma and A.~J. Morton.
\newblock Computational experience with the dual affine variant of
{Karmarkar's} method for linear programming.
\newblock {\em Operations Research Letters}, 6:261--267, 1987.
\bibitem{ipm:Monteiro9}
R.~D.~C. Monteiro.
\newblock Convergence and boundary behavior of the projective scaling
trajectories for linear programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
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Mathematical Society, Providence, Rhode Island, USA, 1990.
\bibitem{ipm:Monteiro10}
R.~D.~C. Monteiro.
\newblock Convergence and boundary behavior of the projective scaling
trajectories for linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):842--858, 1991.
\bibitem{ipm:Monteiro13}
R.~D.~C. Monteiro.
\newblock The global convergence of a class of primal potential reduction
algorithms for convex programming.
\newblock {Technical Report}, Department of Systems and Industrial Engineering,
University of Arizona, Tucson, AZ~85721, USA, August 1991.
\bibitem{ipm:Monteiro8}
R.~D.~C. Monteiro.
\newblock An implementation of range analysis for {LP} problems solved via
interior point methods.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
Janeiro, Brazil}, Department of Systems and Industrial Engineering,
University of Arizona, Tucson, AZ~85721, USA, July 1991.
\bibitem{ipm:Monteiro1}
R.~D.~C. Monteiro.
\newblock On the continuous trajectories for a potential reduction algorithm
for linear programming.
\newblock {\em Mathematics of Operations Research}, 17:225--253, 1992.
\bibitem{ipm:Monteiro11}
R.~D.~C. Monteiro.
\newblock A globally convergent primal--dual interior point algorithm for
convex programming.
\newblock {\em Mathematical Programmingh}, 64:123--147, 1994.
\bibitem{ipm:Monteiro24}
R.~D.~C. Monteiro.
\newblock Primal--dual algorithms for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 7:663--678, 1997.
\newblock Former technical report title (Oct. 1995)\,: Primal--dual
path--following algorithms for semidefinite programming.
\bibitem{ipm:Monteiro32}
R.~D.~C. Monteiro.
\newblock Polynomial convergence of primal--dual algorithms for semidefinite
programming based on {Monteiro and Zhang} family of directions.
\newblock {\em SIAM Journal on Optimization}, 8:797--812, 1998.
\bibitem{ipm:Monteiro2}
R.~D.~C. Monteiro and I.~Adler.
\newblock An ${O(n^{3}L)}$ primal--dual interior point algorithm for linear
programming.
\newblock {Technical Report} ORC~87--4, Department of Industrial Engineering
and Operations Research, University of California, Berkeley, CA~94720, USA,
1987.
\bibitem{ipm:Monteiro6}
R.~D.~C. Monteiro and I.~Adler.
\newblock A polynomial primal--dual affine algorithm for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
USA}, Engineering Systems Research Center, University of California,
Berkeley, CA~94720, USA, October 1988.
\bibitem{ipm:Monteiro3}
R.~D.~C. Monteiro and I.~Adler.
\newblock Interior path following primal--dual algorithms\,: {Part\,I\,:
Linear} programming.
\newblock {\em Mathematical Programming}, 44:27--41, 1989.
\bibitem{ipm:Monteiro4}
R.~D.~C. Monteiro and I.~Adler.
\newblock Interior path following primal--dual algorithms\,: {Part\,II\,:
Convex} quadratic programming.
\newblock {\em Mathematical Programming}, 44:43--66, 1989.
\bibitem{ipm:Monteiro5}
R.~D.~C. Monteiro and I.~Adler.
\newblock An extension of {Karmarkar--type} algorithm to a class of convex
separable programming problems with global linear rate of convergence.
\newblock {\em Mathematics of Operations Research}, 15:408--422, 1990.
\bibitem{ipm:Monteiro7}
R.~D.~C. Monteiro, I.~Adler, and M.~G.~C. Resende.
\newblock A polynomial--time primal--dual affine scaling algorithm for linear
and convex quadratic programming and its power series extension.
\newblock {\em Mathematics of Operations Research}, 15:191--214, 1990.
\bibitem{ipm:Monteiro25}
R.~D.~C. Monteiro and S.~Mehrotra.
\newblock A general parametric analysis approach and its implication to
sensitivity analysis in interior point methods.
\newblock {\em Mathematical Programming}, 72:65--82, 1996.
\bibitem{ipm:Monteiro26}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock Properties of an interior--point mapping for mixed complementarity
problems.
\newblock {\em Mathematics of Operations Research}, 21:629--654, 1996.
\bibitem{ipm:Monteiro29}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock A potential reduction {Newton} method for constrained equations.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
Georgia Technology Institute, Atlanta, GA~30322--0205, USA, March 1997.
\bibitem{ipm:Monteiro35}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock On two interior--point mappings for nonlinear semidefinite
complementarity problems.
\newblock {\em Mathematics of Operations Research}, 23:39--60, 1998.
\bibitem{ipm:Monteiro15}
R.~D.~C. Monteiro, J.-S. Pang, and T.~Wang.
\newblock A positive algorithm for the nonlinear complementarity problem.
\newblock {\em SIAM Journal on Optimization}, 5:129--148, 1995.
\bibitem{ipm:Monteiro14}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Limiting behavior of the derivatives of certain trajectories
associated with a monotone horizontal linear complementarity problem.
\newblock {\em Mathematics of Operations Research}, 21:793--814, 1996.
\bibitem{ipm:Monteiro30}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomial convergence of a new family of primal--dual algorithms for
semidefinite programming.
\newblock {Research Memorandum} 627, The Institute of Statistical Mathematics,
4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, 1996.
\bibitem{ipm:Monteiro31}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomiality of primal--dual algorithms for semidefinite linear
complementarity problems based on the {Kojima--Shindoh--Hara} family of
directions.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
1004:138--152, 1997.
\newblock See also Monteiro and Tsuchiya\,\cite{ipm:Monteiro38}.
\bibitem{ipm:Monteiro21}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Global convergence of the affine scaling method for convex quadratic
programming.
\newblock {\em SIAM Journal on Optimization}, 8:26--58, 1998.
\bibitem{ipm:Monteiro37}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomial convergence of primal--dual algorithms for the
second--order cone program based on the {MZ}--family of directions.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
Georgia Technology Institute, Atlanta, GA~30338, USA, May 1998.
\bibitem{ipm:Monteiro38}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomiality of primal--dual algorithms for semidefinite linear
complementarity problems based on the {Kojima--Shindoh--Hara} family of
directions.
\newblock {\em Mathematical Programming}, 84:39--53, 1999.
\newblock See also Monteiro and Tsuchiya\,\cite{ipm:Monteiro31}.
\bibitem{ipm:Monteiro19}
R.~D.~C. Monteiro, T.~Tsuchiya, and Y.~Wang.
\newblock A simplified global convergence proof of the affine scaling
algorithm.
\newblock {\em Annals of Operations Research}, 46/47:443--482, 1993.
\bibitem{ipm:Monteiro23}
R.~D.~C. Monteiro and Y.~Wang.
\newblock Trust region affine scaling algorithms for linearly constrained
convex and concave programs.
\newblock {\em Mathematical Programming}, 80:283--313, 1998.
\bibitem{ipm:Monteiro12}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock A globally and superlinearly convergent potential reduction interior
point method for convex programming.
\newblock {Technical Report} 92--13, Department of Systems and Industrial
Engineering, University of Arizona, Tucson, AZ~85721, USA, July 1992.
\newblock Also available as {\em Technical Report MSC--P316--0792, Mathematical
and Computer Science Division, Argonne National Laboratory, Argonne,
IL~60439, USA, July 1992}.
\bibitem{ipm:Monteiro20}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock Interior--point algorithms for degenerate linear complementarity
problems.
\newblock {\em Computational Optimization and Applications}, 3:131--155, 1994.
\bibitem{ipm:Monteiro16}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock Local convergence of interior--point algorithms for degenerate
monotone {LCP}.
\newblock {\em Computational Optimization and Applications}, 3:131--155, 1994.
\bibitem{ipm:Monteiro17}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock Superlinear primal--dual affine scaling algorithms for {LCP}.
\newblock {\em Mathematical Programming}, 69:311--333, 1995.
\bibitem{ipm:Monteiro18}
R.~D.~C. Monteiro and S.~J. Wright.
\newblock A superlinear infeasible--interior--point affine scaling algorithm
for {LCP}.
\newblock {\em SIAM Journal on Optimization}, 6:1--18, 1996.
\bibitem{ipm:Monteiro28}
R.~D.~C. Monteiro and P.~R. Zanj{\'a}como.
\newblock Implementation of primal--dual methods for semidefinite programming
based on {Monteiro} and {Tsuchiya} {Newton} directions and their variants.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
Georgia Technology Institute, Atlanta, GA~30322--0205, USA, July 1997.
\bibitem{ipm:Monteiro33}
R.~D.~C. Monteiro and P.~R. Zanj{\'a}como.
\newblock A note on the existence of the {Alizadeh--Haeberly--Overton}
direction for semidefinite programming.
\newblock {\em Mathematical Programming}, 78:393--396, 1997.
\bibitem{ipm:Monteiro36}
R.~D.~C. Monteiro and P.~R. Zanj{\'a}como.
\newblock General interior--point maps and existence of weighted paths for
nonlinear semidefinite complementarity problems.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
Georgia Technology Institute, Atlanta, GA~30322--0205, USA, April 1998.
\bibitem{ipm:Monteiro34}
R.~D.~C. Monteiro and Y.~Zhang.
\newblock A unified analysis for a class of path--following primal--dual
interior--point algorithms for semidefinite programming.
\newblock {\em Mathematical Programming}, 81:281--299, 1998.
\bibitem{ipm:Monteiro22}
R.~D.~C. Monteiro and F.~Zhou.
\newblock On superlinear convergence of infeasible--interior--point algorithms
for linearly constrained convex programs.
\newblock {\em Computational Optimization and Applications}, 8:245--262, 1998.
\bibitem{ipm:Monteiro27}
R.~D.~C. Monteiro and F.~Zhou.
\newblock On the existence and convergence of the central path for convex
programming and some duality results.
\newblock {\em Computational Optimization and Applications}, 10:51--77, 1998.
\bibitem{ipm:Morales1}
J.~L. {Morales--P{\'e}rez} and R.~W.~H. Sargent.
\newblock Numerical experiments with an interior point method for large scale
convex quadratic programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, Centre for Process Systems Engineering, Imperial College, London,
United Kingdom, May 1992.
\newblock See also Morales--P{\'e}rez and Sargent \cite{ipm:Morales2}.
\bibitem{ipm:Morales2}
J.~L. {Morales--P{\'e}rez} and R.~W.~H. Sargent.
\newblock On the implementation and performance of an interior point method for
large sparse convex quadratic programming.
\newblock {\em Optimization Methods and Software}, 1:153--168, 1992.
\bibitem{ipm:More1}
J.~J. Mor{\'e} and S.~J. Wright.
\newblock {\em {Optimization Software Guide}}, volume~14 of {\em Frontiers in
Applied Mathematics}.
\newblock SIAM Publications, Philadelphia, PA~19101, USA, November 1993.
\bibitem{ipm:Morin1}
T.~L. Morin, B.~Haas, and T.~B. Trafalis.
\newblock Implementation of an interior point algorithm for multiobjective
optimization.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
USA}, Department of Mathematics and Computer Science, School of Industrial
Engineering, Purdue University, West Lafayette, IN~47907, USA, May 1990.
\bibitem{ipm:Morin3}
T.~L. Morin, N.~Prabhu, and Z.~Zhang.
\newblock Feasible gradients in the gravitational method for linear
programming.
\newblock {\em Journal of the Operational Research Society of India
(Opsearch)}, 32:253--265, 1995.
\bibitem{ipm:Morin4}
T.~L. Morin, N.~Prabhu, and Z.~Zhang.
\newblock Complexity of the gravitational method for linear programming.
\newblock In {\em Foundations of Software Technology and Theoretical Computer
Science}, volume 1180 of {\em Lecture Notes in Computer Science}, pages
212--223. Springer Verlag, Berlin, Germany, 1996.
\bibitem{ipm:Morin2}
T.~L. Morin and T.~B. Trafalis.
\newblock A polynomial--time algorithm for finding an efficient face of a
polyhedron.
\newblock {Technical Report}, Department of Mathematics and Computer Science,
School of Industrial Engineering, Purdue University, West Lafayette,
IN~47907, USA, 1989.
\bibitem{ipm:Morshedi1}
A.~M. Morshedi and R.~A. Tapia.
\newblock Karmarkar as a classical method.
\newblock {Technical Report} TR~87--7, Department of Mathematical Sciences,
Rice University, Houston, TX~77251, USA, August 1987.
\bibitem{ipm:Mosheyev1}
L.~Mosheyev and M.~Zibulewsky.
\newblock Penalty/barriers multiplier algorithm for semidefinite programming\,:
{Dual} bounds and inplementation.
\newblock {Research Report} 1/96, Optimization Laboratory, Faculty of
Industrial Engineering and Management, Technion, Israel Institute of
Technology, Haifa, Israel, 1996.
\bibitem{ipm:Mulkay1}
E.~L. Mulkay and S.~S. Rao.
\newblock Sequential linear programming with interior--point methods for
large--scale optimization.
\newblock {\em Proceedings of the 1998 39th {AIAA/ASME/ASCE/AHS/ASC}
Structures, Structural Dynamics, and Materials Conference and Exhibit and
{AIAA/ASME/AHS} Adaptive Forum}, Part\,3/4:2175--2180, 1998.
\bibitem{ipm:Mueller1}
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\newblock Implementation of interior point methods on parallel and vector
machines.
\newblock In P.~Gritzmann, R.~Hettich, R.~Horst, and E.~Sachs, editors, {\em
Operations Research '91 (Extended Abstracts of the 16th Symposium on
Operations Research held at the University of Trier, Germany, September
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\newblock On a predictor--corrector method for solving linear programs from
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\newblock {Reports on Computational Mathematics}~34, Department of Mathematics,
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\newblock See also Potra \cite{ipm:Potra11}, which is a combined version of
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F.~A. Potra.
\newblock Polynomial complexity versus fast local convergence for interior
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, Department of Management Sciences, The University of Iowa, Iowa
City, IA~52242, USA, May 1992.
\bibitem{ipm:Potra7}
F.~A. Potra.
\newblock A quadratically convergent infeasible interior--point algorithm for
linear programming.
\newblock {Reports on Computational Mathematics}~28, Department of Mathematics,
The University of Iowa, Iowa City, IA~52242, USA, July 1992.
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F.~A. Potra.
\newblock A quadratically convergent predictor--corrector method for solving
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\newblock {\em Mathematical Programming}, 67:383--406, 1994.
\newblock This is a combined version of Potra \cite{ipm:Potra7,ipm:Potra8}.
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\newblock An infeasible interior--point predictor--corrector algorithm for
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\newblock {\em SIAM Journal on Optimization}, 6:19--32, 1996.
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\newblock An {$O(n\,L)$} infeasible--interior--point algorithm for {LCP} with
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\newblock {\em Annals of Operations Research}, 62:81--102, 1996.
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F.~A. Potra and J.~F. Bonnans.
\newblock Infeasible path following algorithms for linear complementarity
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\newblock {INRIA Research Report} RR--2445, Institute National de Recherche en
Informatique et Automatique (INRIA), F--78153~Roquencourt, France, December
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\newblock To appear in {\em Mathematics of Operations Research}. See also
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F.~A. Potra and R.~Sheng.
\newblock Homogeneous interior--point algorithms for semidefinite programming.
\newblock {Reports on Computational Mathematics}~82, Department of Mathematics,
The University of Iowa, Iowa City, IA~52242, USA, November 1995.
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F.~A. Potra and R.~Sheng.
\newblock A path--following method for {LCP} with superlinearly convergent
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\newblock {Reports on Computational Mathematics}~69, Department of Mathematics,
The University of Iowa, Iowa City, IA~52242, USA, April 1995.
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F.~A. Potra and R.~Sheng.
\newblock Superlinear convergence of a predictor--corrector method for
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\newblock {Reports on Computational Mathematics}~91, Department of Mathematics,
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F.~A. Potra and R.~Sheng.
\newblock Superlinear convergence of interior--point algorithms for
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\newblock {Reports on Computational Mathematics}~86, Department of Mathematics,
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F.~A. Potra and R.~Sheng.
\newblock A large--step infeasible--interior--point method for the
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\newblock {\em SIAM Journal on Optimization}, 7:318--335, 1997.
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\newblock Predictor--corrector algorithms for solving $p_{*}(\kappa)$--matrix
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\newblock {\em Mathematical Programming}, 76:223--244, 1997.
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\newblock Superlinearly convergent infeasible--interior--point algorithm for
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\newblock {\em SIAM Journal on Optimization}, 8:1007--1028, 1998.
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\newblock {SDPHA\,: A MATLAB} implementation of homogeneous interior--point
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\newblock {Reports on Computational Mathematics} 100, Department of
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\newblock {Reports on Computational Mathematics}~23, Department of Mathematics,
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\newblock An interior--point method for linear complementarity problems with
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\newblock {Technical Report} TR~91--23, Department of Mathematical Sciences,
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\newblock {Working Paper} 90--10, Department of Management Sciences, The
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\newblock See also Potra and Ye\,\cite{ipm:Potra10}.
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\newblock Interior point methods for nonlinear complementarity problems.
\newblock {Reports on Computational Mathematics}~15, Department of Mathematics,
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\newblock Revised January 1994. See also Powell \cite{ipm:Powell8}.
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\newblock {Technical Report} (in preparation), Department of Mathematical
Sciences, Rice University, Houston, TX~77251, USA, 1992.
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\newblock On the quadratic convergence of the singular {Newton's} method.
\newblock {\em SIAG/OPT Views--and--News, A forum for the SIAM Activity Group
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R.~A. Tapia, Y.~Zhang, M.~Saltzman, and A.~Weiser.
\newblock The {Mehrotra} predictor--corrector interior--point method as a
perturbed composite {Newton} method.
\newblock {\em SIAM Journal on Optimization}, 6:47--56, 1996.
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\newblock On the convergence of the iteration sequence in primal--dual interior
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\newblock {\em Mathematical Programming}, 68:141--154, 1995.
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\newblock The method of inscribed ellipsoids.
\newblock {\em Soviet Mathematics Doklady}, 37:226--230, 1988.
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\newblock {\em Alkalmazott Matematikai Lapok}, 15:133--162, 1990/91.
\newblock (In Hungarian, English summary).
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\newblock {\em {Interior Point Algorithms of Mathematical Programming}},
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\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
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\newblock An easy way to teach interior--point methods.
\newblock {Technical Report} 98--24, Faculty of Information Technology and
Systems Subfaculty of Technical Mathematics and Informatics, Department of
Statistics, Stochastic and Operations Research Delft University of
Technology, P.O.\,Box\,5031, NL--2600~GA~Delft, The Netherlands, 1998.
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\newblock A note on {Mascarenhas'} counter example about global convergence of
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\newblock {Research Memorandum} 596, The Institute of Statistical Mathematics,
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\newblock Computing maximum likelihood estimators of convex density functions.
\newblock {Technical Report} 95--49, Faculty of Technical Mathematics and
Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.
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R.~G. Thompson, P.~S. Dharmapala, J.~B. Diaz, M.~D. Gonzalez-Lima, and R.~M.
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\newblock {DEA} multiplier analytic center sensitivity with an illustrative
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\newblock An implementation of {Karmarkar's} interior point algorithm.
\newblock {Working Paper} 89--124, Department of Economics and Econometrics,
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\newblock A simple, quadratically convergent interior point algorithm for
linear programming and convex quadratic programming.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
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\newblock The effects of degeneracy and sparsity on {Karmarkar's} projective
algorithm and its variants.
\newblock {Technical Report}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1988.
\newblock See Todd \cite{ipm:Todd9}.
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\newblock {\em Mathematical Programming}, 41:97--113, 1988.
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\newblock Improved bounds and containing ellipsoids in {Karmarkar's} linear
programming algorithm.
\newblock {\em Mathematics of Operations Research}, 13:650--659, 1988.
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M.~J. Todd.
\newblock Polynomial algorithms for linear programming.
\newblock In H.~A. Eiselt, editor, {\em Advances in Optimization and Control,
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\newblock Anticipated behavior of {Karmarkar's} algorithm.
\newblock {Technical Report} 879, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, December 1989.
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M.~J. Todd.
\newblock Recent developments and new directions in linear programming.
\newblock In M.~Iri and K.~Tanabe, editors, {\em Mathematical Programming\,:
Recent Developments and Applications}, pages 109--157. Kluwer Academic Press,
Dordrecht, The Netherlands, 1989.
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\newblock Anticipated behavior of interior point methods for linear
programming.
\newblock {Talk held at the Symposium on Mathematical Programming in
Oberwolfach, Germany}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, January 1990.
\newblock See Todd \cite{ipm:Todd11}, Mizuno et al.\,%
\cite{ipm:Mizuno4,ipm:Mizuno5}.
\bibitem{ipm:Todd5}
M.~J. Todd.
\newblock A {Dantzig--Wolfe--like variant of Karmarkar's} interior--point
linear programming algorithm.
\newblock {\em Operations Research}, 38:1006--1018, 1990.
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M.~J. Todd.
\newblock The effects of degeneracy, null and unbounded variables on variants
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\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
Optimization, Papers from the Workshop held at Cornell University, Ithaca,
NY, USA, October 1989}, volume~46 of {\em SIAM Proceedings in Applied
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(SIAM), Philadelphia, PA, USA, 1990.
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M.~J. Todd.
\newblock Projected scaled steepest descent in {Kojima--Mizuno--Yoshise's}
potential reduction algorithm for the linear complementarity problem.
\newblock {Technical Report} 950, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, December 1990.
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M.~J. Todd.
\newblock The affine--scaling direction for linear programming is a limit of
projective--scaling directions.
\newblock {\em Linear Algebra and Its Applications}, 152:93--105, 1991.
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M.~J. Todd.
\newblock Another derivation of the {Karmarkar} direction for linear
programming.
\newblock {Technical Report} 91--20, Computational Optimization Project, Center
for Applied Mathematics, Cornell University, Ithaca, NY~14853--3801, USA,
December 1991.
\bibitem{ipm:Todd22}
M.~J. Todd.
\newblock Playing with interior points.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
Newsletter}, 19:17--25, August 1991.
\bibitem{ipm:Todd24}
M.~J. Todd.
\newblock Probabilistic models in linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):671--693, 1991.
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M.~J. Todd.
\newblock A low complexity interior point algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:198--209, 1992.
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M.~J. Todd.
\newblock On {Anstreicher's} combined {phase\,I\,--\,phase\,II} projective
algorithm for linear programming.
\newblock {\em Mathematical Programming}, 55:1--15, 1992.
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M.~J. Todd.
\newblock Recent developments on interior point methods for linear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
IL, USA}, School of Operations Research and Industrial Engineering, Cornell
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\newblock There is no underlying report.
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\newblock Combining {phase\,I and phase\,II} in a potential reduction algorithm
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\newblock {\em Mathematical Programming}, 59:133--150, 1993.
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M.~J. Todd.
\newblock A lower bound on the number of iterations of primal--dual
interior--point methods for linear programming.
\newblock {Technical Report} 1050, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, March 1993.
\newblock Revised June 1993.
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\newblock Analysis of interior--point methods for linear programming problems
with variable upper bounds.
\newblock In S.~Gomez and J.~P. Hennart, editors, {\em Advances in Optimization
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Numerical Analysis, Oaxaca, Mexico, 1992)}, volume 275 of {\em Mathematics
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\newblock Interior--point algorithms for semi--infinite programming.
\newblock {\em Mathematical Programming}, 65:217--245, 1994.
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M.~J. Todd.
\newblock On lower bound on the number of iteration of an interior--point
algorithm for linear programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
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\newblock See also Todd and Ye \cite{ipm:Todd33}.
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\newblock Scaling, shifting and weighting in interior--point methods.
\newblock {\em Computational Optimization and Applications}, 3:305--315, 1994.
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M.~J. Todd.
\newblock Theory and practice for interior--point methods.
\newblock {\em ORSA Journal on Computing}, 6:28--31, 1994.
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\newblock On adjusting parameters in homotopy methods for linear programming.
\newblock In {\em Approximation Theory and Optimization}, pages 201--220.
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\newblock On search directions in interior--point methods for semidefinite
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\newblock {Technical Report} 1205, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, October 1997.
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\newblock Potential--reduction methods in mathematical programming.
\newblock {\em Mathematical Programming}, 76:3--45, 1997.
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M.~J. Todd.
\newblock A short history of interior--point methods.
\newblock {Technical Report}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1998.
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\newblock An extension of {Karmarkar's} algorithm for linear programming using
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\newblock {\em Algorithmica}, 1(4):409--424, 1986.
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\newblock An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine
algorithm for linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
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M.~J. Todd and S.~Herzel.
\newblock Interior point algorithms for a class of convex programming problems.
\newblock {Technical Report} 1097, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, June 1994.
\bibitem{ipm:Todd23}
M.~J. Todd, S.~Mizuno, and Y.~Ye.
\newblock Anticipated behavior of path--following algorithms for linear
programming.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
Mathematical Programming, Asilomar, CA, USA}, School of Operations Research
and Industrial Engineering, Cornell University, Ithaca, NY~14853--3801, USA,
February 1990.
\newblock See Mizuno et al.\ \cite{ipm:Mizuno4}.
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M.~J. Todd, K.~Toh, and R.~T{\"u}t{\"u}nc{\"u}.
\newblock On the {Nesterov--Todd} direction in semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:769--796, 1998.
\bibitem{ipm:Todd41}
M.~J. Todd, L.~Tun{\c c}el, and Y.~Ye.
\newblock Probabilistic analysis of two complexity measures for linear
programming problems.
\newblock {Technical Report} TR~1219, School of Operations Research and
Industrial Engineering, Cornell University, Ithaca, NY~14853--3801, USA,
October 1998.
\newblock Also available as {\it{CORR 98--48, Department of Combinatorics and
Optimization, University of Waterloo, Waterloo, Ontario, Canada, October
1998}}.
\bibitem{ipm:Todd20}
M.~J. Todd and J.-Ph. Vial.
\newblock Todd's low--complexity algorithm is a predictor--corrector
path--following method.
\newblock {\em Operations Research Letters}, 11:199--207, 1992.
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M.~J. Todd and Y.~Wang.
\newblock A projective algorithm for convex quadratic programming.
\newblock {Technical Report}, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1991.
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M.~J. Todd and Y.~Wang.
\newblock On combined {phase\,I\,--\,phase\,II} projective methods for linear
programming.
\newblock {\em Algorithmica}, 9(1):64--83, 1993.
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M.~J. Todd and Y.~Ye.
\newblock A centered projective algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 15:508--529, 1990.
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M.~J. Todd and Y.~Ye.
\newblock A lower bound on the number of iterations of long--step primal--dual
linear programming algorithms.
\newblock {\em Annals of Operations Research}, 62:233--252, 1996.
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\newblock Approximate {Farkas Lemmas} and stopping rules for iterative
infeasible--point algorithms for linear programming.
\newblock {\em Mathematical Programming}, 81:1--21, 1998.
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\newblock Search directions for primal--dual interior point methods in
semidefinite programming.
\newblock {Technical Report}, Department of Mathematics, National University of
Singapore, Singapore~0511, July 1997.
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K.~C. Toh, M.~J. Todd, and R.~H. T{\"u}t{\"u}nc{\"u}.
\newblock {SDPT3 -- A MATLAB software package for semidefinite programming}.
\newblock {Manuscript}, School of Operations Research and Industrial
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\newblock Cahier~82, Laboratoire de Analyse et Modelisation de Systemes pour
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\newblock (In French).
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\newblock New numerical results on {Karmarkar's} algorithm.
\newblock Cahier, Laboratoire de Analyse et Modelisation de Systemes pour
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F--75775~Paris~Cedex~16, France, 1988.
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\newblock In C.~Brezinski, editor, {\em Numerical and Applied Mathematics,
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\newblock {\em Mathematical Programming Study}, 31:175--191, 1987.
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\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
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\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami, FL,
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\newblock {Research Report} 89--B--5, Graduate School for Policy Science,
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\newblock {\em Computers and Mathematics with Applications}, 20(2):1--7, 1990.
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\newblock {\em Proceedings of the 1996 Canadian Conference on Electrical and
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\newblock {\em Efficient faces of a polytope\,: {Interior} methods in multiple
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\newblock PhD thesis, Department of Mathematics and Computer Science, School of
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T.~B. Trafalis.
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
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T.~B. Trafalis and N.~P. Cou{\"e}llan.
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\newblock Also available as\,: Technical Report 1135, School of Operations
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\newblock {Unpublished Manuscript}, Department of Civil Engineering and
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
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\newblock {\em Mathematics of Operations Research}, 20:163--174, 1995.
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\newblock {LOQO\,: An} interior point code for quadratic programming.
\newblock {Technical Report} SOR--94--15, Department of Civil Engineering and
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\newblock {\em SIAM Journal on Optimization}, 5:100--113, 1995.
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\newblock {\em Linear Programming\,: Foundations and Extensions}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
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\newblock {Technical Report} SOL~96--07, Department of Civil Engineering and
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\newblock Symmetric indefinite systems for interior point methods.
\newblock {\em Mathematical Programming}, 58:1--32, 1993.
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R.~J. Vanderbei, A.~Duarte, and B.~Yang.
\newblock An algorithmic and numerical comparison of several interior--point
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\newblock {Technical Report} SOR--94--05, Department of Civil Engineering and
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\newblock {Working Paper}, Department of Management Science, University of
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\newblock {Technical Report}, Department of Management Science, University of
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\newblock Complexity analysis of the analytic center cutting plane method that
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\newblock {\em Mathematical Programming}, 78:85--104, 1997.
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\newblock {\em {Interior--Point Algorithms\,: Theory and Practice}}.
\newblock John Wiley\,\&\, Sons, New York, USA, 1997.
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\newblock {Working Paper}, Department of Management Science, University of
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\newblock On the complexity of approximating a {KKT} point of quadratic
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\newblock {\em Mathematical Programming}, 84:219--226, 1999.
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\newblock On quadratic and ${O(\sqrt{n} L)}$ convergence of a
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\newblock {\em Mathematical Programming}, 62:537--551, 1993.
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\newblock Recovering the shadow price in projection methods for linear
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\newblock {Technical Report}, Department of Management Science, University of
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Y.~Ye, O.~G{\"u}ler, R.~A. Tapia, and Y.~Zhang.
\newblock A quadratically convergent ${O(\sqrt{n}L)}$--iteration algorithm for
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\newblock {\em Mathematical Programming}, 59:151--162, 1993.
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\newblock Further results on build--up approaches for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in, Anaheim, CA,
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\newblock Recovering optimal dual solutions in {Karmarkar's} polynomial
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\newblock {\em Mathematical Programming}, 39:305--317, 1987.
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\newblock Near--boundary behavior of primal--dual potential reduction
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\newblock {\em Mathematical Programming}, 58:243--255, 1993.
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\newblock A class of linear complementarity problems solvable in polynomial
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\newblock {\em Linear Algebra and Its Applications}, 152:3--17, 1991.
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Y.~Ye and F.~A. Potra.
\newblock An interior--point algorithm for solving entropy optimization
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\newblock {Working Paper Series} 90--22, Department of Management Science,
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\newblock Same as Potra and Ye \cite{ipm:Potra5}.
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\newblock A superlinearly convergent ${O(\sqrt{n}L)}$--iteration algorithm for
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\newblock {Technical Report} TR--91--22, Department of Mathematical Sciences,
Rice University, Houston, TX~77251, USA, 1991.
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Y.~Ye and M.~J. Todd.
\newblock Containing and shrinking ellipsoids in the path--following algorithm.
\newblock {\em Mathematical Programming}, 47:1--10, 1990.
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Y.~Ye, M.~J. Todd, and S.~Mizuno.
\newblock An {$O(\sqrt{n} L)$}--iteration homogeneous and self--dual linear
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\newblock {\em Mathematics of Operations Research}, 19:53--67, 1994.
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\newblock A polynomial--time algorithm for convex quadratic programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
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\newblock An extension of {Karmarkar's} projective algorithm for convex
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\newblock {\em Mathematical Programming}, 44:157--179, 1989.
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Q.~J. Yeh.
\newblock {\em A reduced dual affine scaling algorithm for solving assignment
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\newblock PhD thesis, Department of Industrial Engineering and Operations
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S.~D. Yen and W.~S. Levine.
\newblock Mixed {$H_{2H}$} infinity optimization\,: {A BMI} solution.
\newblock {\em Proceedings of the 1997 36th IEEE Conference on Decision and
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\newblock An optimization method for convex programming problems -- the
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\newblock {\em Systems Control and Informations}, 38:155--160, 1994.
\newblock (In Japanese).
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\newblock Complementarity problems.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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\newblock A new {OPF} (optimal power flow) algorithm based on {Karmarkar's}
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\newblock {\em Proceedings of the Chinese Society of Electrical Engineering},
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\newblock (In Chinese).
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\newblock High--order large--step interior--point algorithms for linear
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\newblock {Research Report} 650, Department of Mathematics, National University
of Singapore, Singapore~0511, 1994.
\newblock Identical to Zhao\,\cite{ipm:Zhao9}.
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Z.~G. Yun and Z.~W. Liu.
\newblock A line--search method for {Lagrangian} relexation ascent algorithms.
\newblock {Research Report} 644, Department of Mathematics, National University
of Singapore, Singapore~0511, 1994.
\newblock Identical to Zhao and Liu\,\cite{ipm:Zhao10}.
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\newblock {\em Applied Mathematics---A Journal of Chinese Universities},
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\newblock Exact shifts of the constraints in methods of centers.
\newblock {\em Akademiya Nauk Respubliki Moldova Izvestiya Matematika}, pages
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\newblock Data--level parallel computing with interior point algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
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\newblock See Eckstein et al.\ \cite{ipm:Eckstein1}.
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\newblock Massively parallel solution of robust optimization programs via
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\newblock {Talk held at the INFORMS Joint National Meeting in Los Angeles, CA,
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\newblock Dual barrier--projection and barrier--{Newton} methods in linear
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\newblock In J.~Dolezal et~al., editor, {\em System Modelling and Optimization
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\newblock {Research Report} 93--13, Department of Mathematics and Statistics,
University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA, July
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\newblock A {Mehrotra}--type predictor--corrector algorithm with polynomiality
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\newblock {\em Annals of Operations Research}, 62:131--150, 1996.
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\newblock The affine transformation method and the path following method for
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\newblock {\em Chinese Journal of Operations Research}, 8(2):25--34, 1989.
\newblock (In Chinese).
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\newblock On the convergence property of {Iri--Imai's} method for linear
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\newblock {Technical Report} 8917/A, Economic Institute, Erasmus University,
Rotterdam, The Netherlands, 1989.
\newblock See also Zhang \cite{ipm:SZhang1}.
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\newblock The convergence property of the {Iri--Imai} algorithm for some smooth
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\newblock {\em Journal of Optimization Theory and Applications}, 82:121--138,
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\newblock See also Zhang \cite{ipm:Zhang4}.
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\newblock On the polynomiality of {Iri and Imai's} new algorithm for linear
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\newblock {\em Journal of Qinhua University}, 28:121--126, 1988.
\newblock (In Chinese).
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\newblock A homotopy interior algorithm for posynomial geometric programming.
\newblock {\em Mathematica Numerica Sinica}, 18:225--232, 1996.
\newblock (In Chinese).
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\newblock Interior point method for solving optimization problems.
\newblock {\em Proceedings of the International Conference on Intelligent
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\newblock An optimization method based on a primal--dual interior point
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\newblock {\em Journal of the Huazhong University of Science and Technology},
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\newblock (In Chinese).
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\newblock Super--linear convergence of interior point algorithms for a class of
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
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\newblock A primal--dual interior point approach for computing the $\ell_{1}$
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\newblock {\em Journal of Optimization Theory and Applications},
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\newblock {LIPSOL -- A MATLAB} toolkit for linear programming interior--point
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\newblock {Technical Report}, Department of Mathematics and Statistics,
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\newblock See also Zhang \cite{ipm:Zhang23}.
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\newblock On the convergence of a class of infeasible interior--point methods
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\newblock {\em SIAM Journal on Optimization}, 4:208--227, 1994.
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\newblock User's guide to {LIPSOL}.
\newblock {Technical Report}, Department of Mathematics and Statistics,
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\newblock See also Zhang \cite{ipm:Zhang24}.
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\newblock Solving large--scale linear programs by interior--point methods under
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\newblock {Technical Report} 96--01, Department of Mathematics and Statistics,
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\newblock On extending primal--dual interior--point algorithms from linear
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\newblock {\em SIAM Journal on Optimization}, 8:365--386, 1998.
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\newblock A modified predictor--corrector algorithm for locating weighted
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\newblock {\em Journal of Optimization Theory and Applications}, 80:319--331,
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Y.~Zhang and R.~A. Tapia.
\newblock A quadratically convergent polynomial primal--dual interior--point
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\newblock {Technical Report} TR~90--40, Department of Mathematical Sciences,
Rice University, Houston, TX~77251, USA, 1990.
\newblock To appear in {\em SIAM Journal on Optimization 3 (1993)}.
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\newblock On the convergence of interior--point methods to the center of the
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\newblock {Technical Report} TR~91--30, Department of Mathematical Sciences,
Rice University, Houston, TX~77251, USA, 1991.
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\newblock A polynomial--time and superlinearly convergent interior point
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\newblock {Technical Report}, Department of Mathematical Sciences, Rice
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\newblock To appear in {\em SIAM Journal on Optimization, 1992}.
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\newblock Superlinear and quadratic convergence of primal--dual interior--point
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\newblock {\em Journal of Optimization Theory and Applications},
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\newblock On the superlinear and quadratic convergence of primal--dual interior
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\newblock {\em SIAM Journal on Optimization}, 2(2):304--324, 1992.
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\newblock On the superlinear convergence of interior point algorithms for a
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\newblock {\em SIAM Journal on Optimization}, 3(2):413--422, 1993.
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\newblock Superlinear convergence of infeasible interior--point methods for
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\newblock {\em Mathematical Programming}, 66:361--377, 1994.
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\newblock On polynomiality of the {Mehrotra}--type predictor--corrector
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\newblock {\em Mathematical Programming}, 68:303--318, 1995.
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G.~Y. Zhao.
\newblock {\em Estimating the complexity of path--following methods in linear
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\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
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\newblock Large--step path--following primal--dual algorithms for linear
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\newblock {Research Report} 613, Department of Mathematics, National University
of Singapore, Singapore~0511, March 1994.
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G.~Y. Zhao.
\newblock High--order large--step interior point algorithms for linear
complementary problems.
\newblock {Research Report} 650, Department of Mathematics, National University
of Singapore, Singapore~0511, 1995.
\newblock Identical to Yun\,\cite{ipm:Yun1}.
\bibitem{ipm:Zhao7}
G.~Y. Zhao.
\newblock On the choice of parameters for power--series interior point
algorithms in linear programming.
\newblock {\em Mathematical Programming}, 68:49--71, 1995.
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G.~Y. Zhao.
\newblock Interior point methods with decomposition for linear programs.
\newblock {Research Report} 686, Department of Mathematics, National University
of Singapore, Singapore~0511, 1996.
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G.~Y. Zhao.
\newblock Relationship between the curvature integral and the complexity of
path--following methods in linear programming.
\newblock {\em SIAM Journal on Optimization}, 6:57--73, 1996.
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G.~Y. Zhao.
\newblock Log--barrier decomposition methods for solving two--stage stochastic
programs.
\newblock {Research Report} 711, Department of Mathematics, National University
of Singapore, Singapore~0511, June 1997.
\newblock Revised June 1998.
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\newblock Barrier function in the {Lagrangian} dual method for solving
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\newblock {Research Report}, Department of Mathematics, National University of
Singapore, Singapore~0511, 1998.
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G.~Y. Zhao.
\newblock Interior point algorithms for linear complementarity problems based
on large neighborhoods of the central path.
\newblock {\em SIAM Journal on Optimization}, 8:397--413, 1998.
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\newblock A line search method for {Lagrangian} relaxation ascent algorithms.
\newblock {Technical Report} 644, Department of Mathematics, National
University of Singapore, Singapore~0511, 1995.
\newblock Identical to Yun and Liu\,\cite{ipm:Yun2}.
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G.~Y. Zhao and J.~Stoer.
\newblock Estimating the complexity of path--following methods for solving
linear programs by curvature integrals.
\newblock {\em Applied Mathematics~{\&}~Optimization}, 27(1):85--103, 1993.
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G.~Y. Zhao and J.~Sun.
\newblock On the rate of local convergence of higher--order
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strictly complementary solutions}.
\newblock {Research Report} 698, Department of Mathematics, National University
of Singapore, Singapore~0511, March 1997.
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G.~Y. Zhao, J.~Sun, and J.~Zhu.
\newblock A primal--dual affine scaling algorithm with necessary centering as a
safeguard.
\newblock {\em Optimization}, 35:333--343, 1995.
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G.~Y. Zhao and J.~Zhu.
\newblock Analytical properties of the central trajectory in interior point
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\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
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Applications}, pages 362--375. Kluwer Academic Publishers, Dordrecht, The
Netherlands, 1994.
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G.~Y. Zhao and J.~Zhu.
\newblock The curvature integral and the complexity of linear complementarity
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\newblock {\em Mathematical Programming}, 70:107--122, 1995.
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\newblock A classification of trajectory optimization algorithms.
\newblock {Technical Report} 91/115, Minnesota Supercomputer Institute,
University of Minnesota, Minneapolis, MN~55415, USA, April 1991.
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\newblock On the complexity of linear programming problems.
\newblock {\em Chinese Journal of Operations Research}, 7(2):1--10, 1988.
\newblock (In Chinese).
\bibitem{ipm:Zhou1}
J.~Zhou, N.~Xu, and W.~Chen.
\newblock Discussion on {Karmarkar's} method for solving unstandard model.
\newblock {\em Journal of Southeastern University (Nanjing, PR China), English
Edition}, 5(1):38--45, 1989.
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J.~Zhu.
\newblock A path following algorithm for a class of convex programming
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\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
Operations Research}, 36(4):539--377, 1992.
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J.~Zhu and S.~Huang.
\newblock On the convergence rate of the duality gap in a symmetric
primal--dual potential reduction algorithm.
\newblock {\em Operations Research Letters}, 11:289--291, 1992.
\bibitem{ipm:Zhu1}
J.~Zhu and K.~O. Kortanek.
\newblock A polynomial path--following algorithm for linearly constrained
convex programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
PA, USA}, College of Business Administration, University of Iowa, Iowa City,
IA~52240, USA, October 1990.
\bibitem{ipm:Zikan1}
K.~Zikan and R.~W. Cottle.
\newblock The box method for linear programming, {Part\,I\,: Basic} theory.
\newblock {Technical Report}, Systems Optimization Laboratory, Department of
Operations Research, Stanford University, Stanford, CA~94305--4022, USA,
1987.
\bibitem{ipm:Zikan2}
K.~Zikan and R.~W. Cottle.
\newblock The box method for linear programming, {Part\,II\,: Treatment} of
problems in standard form with explicitly bounded variables.
\newblock {Technical Report}, Systems Optimization Laboratory, Department of
Operations Research, Stanford University, Stanford, CA~94305--4022, USA,
1987.
\bibitem{ipm:Zikan3}
K.~Zikan and R.~W. Cottle.
\newblock Solving linear programs with the box method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
USA}, Systems Optimization Laboratory, Department of Operations Research,
Stanford University, Stanford, CA~94305--4022, USA, April 1988.
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U.~Zimmermann.
\newblock On recent developments in linear programming.
\newblock In K.~H. Hoffmann, J.~B. Hiriat-Urruty, C.~Lemarechal, and J.~Zowe,
editors, {\em Trends in Mathematical Optimization\,: Proceedings of the 4th
French--German Conference on Optimization in Irsee, Germany, April 1986},
volume~84 of {\em International Series of Numerical Mathematics}, pages
353--390. Birkh{\"a}user Verlag, Basel, Switzerland, 1988.
\bibitem{ipm:Zimmermann2}
U.~Zimmermann.
\newblock Search directions for projective methods.
\newblock {Technical Report}, Technische Universit{\"a}t Braunschweig, Institut
f{\"u}r Angewandte Mathematik, Abt.\ f{\"u}r Math.\ Optimierung,
Pockelstr.~14, D--3300~Braunschweig, Germany, February 1989.
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U.~Zimmermann.
\newblock Search directions for a class of projective methods.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
Operations Research}, 34:353--379, 1990.
\bibitem{ipm:Zimmermann4}
U.~Zimmermann and C.~Wallacher.
\newblock An interior point method for flow problems.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Technische
Universit{\"a}t Braunschweig, Institut f{\"u}r Angewandte Mathematik, Abt.\
f{\"u}r Math.\ Optimierung, Pockelstr.~14, D--3300~Braunschweig, Germany,
August 1990.
\newblock See also Wallacher and Zimmermann \cite{ipm:Wallacher1}.
\end{thebibliography}