Subject: NA Digest, V. 96, # 16 NA Digest Sunday, April 21, 1996 Volume 96 : Issue 16 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: l(infinity) Algorithm Elliptic PDE Solver Question on Kronecker Products Object Oriented MPI, OOMPI New Book on Total Positivity New Book on Linear-Quadratic Optimization New Book on Singularly Perturbed Diffferential Equations Midwest Numerical Analysis Day IMACS Seminar on Monte Carlo Methods SIAM Conference on Sparse Matrices Modeling Workshop Using GAMS Faculty Position at Technische Univ. Dresden Positions at Auto-trol Technology European Community Research Training Grant Positions at Australian National University Hans Lewy Postdoctoral Fellowship at LBNL Contents, SIAM Optimization Submissions for NA Digest: Mail to na.digest@na-net.ornl.gov. Information about NA-NET: Mail to na.help@na-net.ornl.gov. URL for the World Wide Web: http://www.netlib.org/na-net/na_home.html ------------------------------------------------------- From: Samir Elhedhli Date: Sun, 14 Apr 1996 16:40:53 +0400 (EET DST) Subject: l(infinity) Algorithm Hello, I am currently interested in designing an algorithm for the l_infinity problem (Chebychev, minimax) and I need some algorithm to compare with. If possibe, I want copies of the famous Barrodale-Phillips and Conn-Bartels and Charalambous algorithm. Also if there is any other efficient algorithm, I would like to have information about it. Yours sincerely Samir Elhedhli Department of Industrial Engineering Bilkent University 06533 Ankara Turkey. ------------------------------ From: Fred Kus Date: Tue, 16 Apr 1996 13:08:26 -0400 Subject: Elliptic PDE Solver Hi, I am looking for a solver for the 3D self-adjoint elliptic PDE : div[E(x,y,z)*grad(U(x,y,z))] = R(x,y,z) where E & R are user-specified functions. I am interested in Cartesian as well as cylindrical coordinates. Any suggestions or source code will be appreciated. Thanks in advance. Fred Fred W. Kus INTERNET: fred@McMaster.CA Computing & Information PHONE: (905) 525-9140 ext. 24160 Services FAX (905) 528-3773 McMaster University A. N. Bourns Bldg. Rm 131C Hamilton, Canada L8S 4M1 ------------------------------ From: Raghavendra K. Madyastha Date: Thu, 18 Apr 1996 10:31:24 -0500 (CDT) Subject: Question on Kronecker Products Hi, I have a question related to minimization of a function involving kronecker products and I can't seem to be able to crack it. I've looked in lots of matrix analysis books for similar problems with little luck. I was wondering if anyone had seen something similar to the problem I will pose below. Convention: lower case letters -- vectors (or scalars, if specified) upper case letters -- matrices a^H -- conjugate transpose of 'a' .kron. -- symbol for kronecker product of 2 matrices Problem formulation: minimize f(p,u) = (p^H .kron. u^H)*(E*E^H)*(p .kron. u) subject to p^H*p = 1 and u^H*u = 1 'p' -- m x 1 'u' -- n x 1 'E' -- mn x k Any insight or suggestions on this problem would be greatly appreciated. Thank you. Raghu Madyastha email: raghu666@rice.edu Dept. of Electrical and Computer Engg, Ph: 713-527-8750 x3577 Rice University, P.O.Box 1892, Houston, TX 77251 ------------------------------ From: Jeff Squyres Date: Sun, 21 Apr 1996 17:54:52 -0500 (EST) Subject: Object Oriented MPI, OOMPI The Laboratory for Scientific Computing of the Department of Computer Science and Engineering at the University of Notre Dame is proud to [finally] announce Object Oriented MPI (OOMPI): A full-featured class library for MPI. Some of OOMPI's features include: Full MPI-1.1 functionality Implemented as a thin layer on top of the C MPI bindings Offers convienent and intuitive object-oriented abstractions for message passing Uses many of the powerful semantic features of the C++ language, such as data typing, polymorphism, etc. Full information, documentation, and the source code distribution for OOMPI Version 1.0 can be obtained from: http://www.cse.nd.edu/~lsc/research/oompi/ Any questions, comments, and most especially feedback can be directed to oompi@lsc.nd.edu. Jeff Squyres squyres@cse.nd.edu ------------------------------ From: gasca@posta.unizar.es (Mariano Gasca) Date: Mon, 15 Apr 1996 17:53:56 +0100 Subject: New Book on Total Positivity New book on the applications of Total Positivity. The book Total Positivity and its Applications, (ISBN 0-7923-3924-X) has just been published by Kluwer Academic Pub., Dordrecht, The Netherlands, in the series Mathematics and its Applications. Edited by Mariano Gasca and Charles A. Micchelli, the volume (about 500 pages) contains articles that document the advances in the subject of Total Positivity during the last two decades. The material is divided into ten chapters: Spline Functions, Matrix Theory, Geometric Modeling, Probability and Mathematical Biology, Approximation Theory, Complex Analysis, Statistics, Real Analysis, Combinatorics and Integral Equations. Some of the articles are of a survey nature and others present new results. The book, dedicated by the editors to Prof. S. Karlin, author of the influential treatise Total Positivity (Stanford U. Press) in 1968, is the result of an international meeting held in Jaca (Spain) in September 1994. It is expected that the book will be of value to mathematicians, engineers and computer scientists whose work involves applications of Total Positivity. ------------------------------ From: Vasile Sima Date: Tue, 16 Apr 1996 07:32:45 +0200 Subject: New Book on Linear-Quadratic Optimization NEW BOOK ANNOUNCEMENT: Algorithms for Linear-Quadratic Optimization by Vasile Sima Vol. 200 in "Monographs and Textbooks in Pure and Applied Mathematics" Earl J. Taft and Zuhair Nashed (Series Editors). Publisher: Marcel Dekker, Inc., New York March 1996 / 384 pages, illustrated / Hardcover / ISBN 0-8247-9612-8 This book offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems, providing an overview of recent advances in control and systems theory, numerical linear algebra, and optimization. It covers fundamental issues in control theory and applications, such as regulator and estimator design, state estimation, and robust control. Topics of special interest, including H-infinity and H-2 optimization, defect correction, stability-enhancing scaling procedure for Schur Riccati solvers, Hammarling's algorithms for non-negative definite Lyapunov equations, ordering generalized real Schur forms, structure- preserving techniques, finding eigenvalues of Hamiltonian matrices, and multishift algorithms, are highlighted. Theoretical treatment benefically combines with an insight into algorithmic techniques, with relevant numerical issues, advanced software tools, implementation details improving performances, practical recommendations, and solution of specific problems. The chapters have a similar organization: basic theory (with short proofs); mathematical and computational problem(s); and associated numerical solvers. Each particular solver has the following referred: algorithmic templates; computational issues; applicability and limitations. To be as self-contained as possible, the book includes and examines state-of-the-art numerical linear algebra algorithms and associated software tools, like LAPACK. All algorithms are written in a suggestive and concise informal language, that facilitates computer implementation. A summary of extensive numerical comparisons of various algorithms is included. Many worked numerical examples, based on published industrial models, are used for illustrative purposes. The book also contains 20 figures, 11 tables, an index of algorithm definitions (with over 80 entries), a subject index, and about 300 references. By its emphasis on the latest algorithmic advances and areas of current research interest, as well as by its broad coverage, methodological guidances and practical guidelines, the book could be useful to applied and industrial mathematicians, control engineers, electrical and electronics engineers, computer programmers, researchers in automatic control and dynamical optimization, and graduate students in these disciplines. CONTENTS 1 Linear-Quadratic Optimization Problems 2 Newton Algorithms 3 Schur and Generalized Schur Algorithms 4 Structure-Preserving Algorithms A Comparison of Riccati Solvers B Notation and Abbreviations Additional information can be obtained from: Promotion Department Marcel Dekker, Inc. or Hutgasse 4, Postfach 812, 270 Madison Avenue, CH-4001 Basel New York, N.Y. 10016 Switzerland (212) 696-9000 Phone 061-261-8482 ------------------------------ From: Lutz Tobiska Date: Wed, 17 Apr 1996 18:07:42 +0200 (MESZ) Subject: New Book on Singularly Perturbed Diffferential Equations Springer-Verlag have just published the book "NUMERICAL METHODS FOR SINGULARLY PERTURBED DIFFFERENTIAL EQUATIONS Convection-Diffusion and Flow Problems" by Hans-Goerg Roos, Martin Stynes & Lutz Tobiska. Springer Series in Computational Mathematics No. 24 Published March 1996 in Heidelberg, Germany, ISBN 3-540-60718-8, 350 pages, cost 148 DM. This book collects, explains and analyses basic methods and recent results for the successful numerical solution of singularly perturbed differential equations. Such equations model many physical phenomena and their solutions are characterized by the presence of layers. The book is a wide-ranging introduction to the exciting current literature in this area. It concentrates on linear convection-diffusion equations and related nonlinear flow problems, encompassing both ordinary and partial differential equations. While many numerical methods are considered, particular attention is paid to those with realistic error estimates. The book provides a solid and thorough foundation for the numerical analysis and solution of singular perturbation problems. The full Table of Contents is available as a postscript file on the WorldWideWeb: open Martin Stynes's home page at http://ogham.ucc.ie/~martin/ then follow the link to Publications. Prof. Dr. Lutz Tobiska | Otto-von-Guericke Universitaet Magdeburg | Tel: +49-391-671 8650 Institut fuer Analysis und Numerik | Postfach 4120 , Magdeburg, D-39016 | Fax: +49-391-671 8073 email: lutz.tobiska@mathematik.uni-magdeburg.d400.de ------------------------------ From: Bruce A Wade Date: Tue, 16 Apr 1996 16:40:35 -0500 (CDT) Subject: Midwest Numerical Analysis Day The Midwest Numerical Analysis Day of 1996 will be held on Saturday, April 27 at the University of Wisconsin- Milwaukee. Information can be obtained on the World Wide Web at http://www.math.uwm.edu The featured speakers are: Kendall Atkinson, University of Iowa A survey of recent work in the numerical solution of boundary integral equations Suhrit K. Dey, Eastern Illinois University Solving Nonlinear Systems by perturbed Functional Iterations Donald Greenspan, University of Texas-Arlington Discrete Modeling A complete list of speakers is available on the Web page. ------------------------------ From: R. Beauwens Date: Wed, 17 Apr 1996 15:57:09 +0200 (DST) Subject: IMACS Seminar on Monte Carlo Methods IMACS SEMINAR ON MONTE CARLO METHODS APRIL 1-3, 1997 BRUSSELS, BELGIUM FIRST CALL FOR CONTRIBUTIONS An IMACS Seminar on Monte Carlo methods will be held at Brussels Free University (ULB) from April 1 to 3, 1997, jointly organised by IMACS and ULB. The purpose of the seminar is to provide a forum for the presentation of recent advances in the analysis, implementation and applications of Monte Carlo simulation techniques and, in particular to stimulate the exchange of informations between specialists in these areas. The topics should cover both theoretical developments: - random numbers - statistical analysis - variance reduction - perturbation techniques - MC error analysis and application fields: - particle transport - reliability analysis - quantum mechanics - statistical physics We are now calling for original contributions describing new results. A few tutorial review works can also be accepted. International Program Committee: Prof. K. Binder, Johannes Gutenberg-Universität Mainz, Germany. Dr. T. Booth, Lawrence Livermore National Laboratory, USA. Prof. J.M. Caillol, Université Paris XI Orsay, France. Prof. D. Ceperley, University of Illinois at Urbana-Champaign, USA. Prof. I. Dimov, Bulgarian Academy of Sciences, Bulgaria. Prof. A. Dubi, Ben Gurion University of the Neguev, Israel. Dr. W. Eckstein, Max-Planck-Institut für Plasmaphysik, Garching, Germany. Dr. A. Gandini, ENEA-CRE Casaccia, Roma, Italy. Prof. J.H. Halton, The University of North Carolina at Chapel Hill, USA. Prof. M.H. Kalos, Cornell University, USA. Prof. S.E. Koonin, The California Institute of Technology, USA. Prof. D. Levesque, Université Paris XI Orsay, France. Prof. J.D. Lewins, University of Cambridge, United Kingdom. Prof. E.E. Lewis, Northwestern University, USA. Prof. M. Marseguerra, Politecnico di Milano, Italy. Prof. W.R. Martin, University of Michigan, USA. Prof. J.W. Negele, Massachusetts Institute of Technology, USA. Dr. F. Salvat, Universitat de Barcelona, Spain. Dr. S. Seltzer, National Institute of Standards and Technology, USA. Prof. J. Spanier, Claremont Graduate School, USA. Dr. I.M. Sobol, Russian Academy of Sciences, Russia. Prof. S. Tougaard, University of Odense, Denmark. Prof. P.A. Whitlock, Brooklyn College, USA. To be on our mailing list and get further informations, please see our server: http://mnserver.ulb.ac.be/Seminar.html Seminar address: Alain Dubus IMACS Monte Carlo Seminar ULB, CP165 50, av. F.D. Roosevelt B-1050 Brussels mtc@metronu.ulb.ac.be ------------------------------ From: Trini Flores Date: Sat, 20 Apr 96 11:31:54 EST Subject: SIAM Conference on Sparse Matrices Second SIAM Conference on SPARSE MATRICES October 9-11, 1996 The Coeur d'Alene Resort Coeur d'Alene, Idaho Deadline for submission of one-page extended abstracts: MAY 15, 1996. Electronic submissions in LaTeX or ASCII files are encouraged. Send completed abstracts to: meetings@siam.org esmond@msr.epm.ornl.gov dpierce@espresso.rt.cs.boeing.com Information regarding the conference can be accessed in electronic format via SIAM's World Wide Web: http://www.siam.org/meetings/sm96/sm96home.htm ------------------------------ From: Jerome Kreuser Date: Sun, 21 Apr 1996 20:10:03 -0400 (EDT) Subject: Modeling Workshop Using GAMS Announcing a Workshop on Mathematical Programming Modeling in Economics, Finance, and Projects Using the General Algebraic Modeling System (GAMS) Sponsored by the George Washington University Research and Applications on Modeling Laboratory, Department of Operations Research, and the SEAS Computing Facility. May 20-23, 1996 in Washington, D.C. For more information see http://www.seas.gwu.edu/seas/projects/ramlab/ Or email to ramlab@seas.gwu.edu ------------------------------ From: Jean Utke Date: Mon, 15 Apr 1996 17:08:13 +0200 Subject: Faculty Position at Technische Univ. Dresden Technical University Dresden C3-Professorship for High Performance Computing to be filled at the Faculty of Mathematics and Science, Dept. of Mathematics, Institute of Scientific Computing. The Technical University established this position in the context of the acquisition of a high performance computer. The professor will be the founding director of the interdisciplinary center for high performance computing. The prospective professor should follow the latest developments in high performance computing and be involved in the development of new algorithms and implementations. He/she will support other university departments with respect to teaching and research that requires the use of high performance computers. He/she is also expected to advise the partners inside and outside the university regarding the development and use of centralized and distributed computing resources. In addition to publications and lectures, supervision of interdisciplinary Diploma and PhD theses are expected. Habilitation or comparable experience in the area of High Performance Computing are required. The applicant must satisfy the employment conditions according to o51 SHG (Tertiary Education Law of the State of Saxony) from 8/4/93. Women are especially encouraged to apply. Applications from handicapped persons will be given particular consideration. The application should consist of a Curriculum Vitae, an outline of scientific background, a photo, lists of scientific publications and a copy of the highest academic degree obtained. Applications must be received no later than 4/30/96 by : TU Dresden, Dekan der Fakultaet Mathematik und Naturwissenschaften, Herr Prof. Dr. R. Kuehne, 01062 Dresden, GERMANY. ------------------------------ From: Christine Copello Date: Tue, 16 Apr 96 07:52:00 PDT Subject: Positions at Auto-trol Technology Auto-trol Technology Corporation located in Denver, CO is a systems integrator on the forefront of graphics and information technology. Auto-trol implements distributed computer systems in industrial companies and government agencies worldwide. Presently, we have opportunitites for the following positions: Software Development Engineer (All levels) C++ required, some experience with CAD packages a plus, MOTIF a plus. Software Test Engineers Experience using automated test development preferably X-runner, data base experience helpful and experience developing test plans/procedures. Technical Writer Technical writing experience in a high technology environment required. Network Communication Software Engineer Strong analytical and problems skills, UNIX experience, including shell scripts; Oracle database experience, C programming. Experience in the following areas are a plus: C++ programming; knowledge of network management, including LAN, WAN and telecommunications. Interested candidates should send a resume and salary history to: Auto-trol Technology Corporation 12500 N. Washington Street Denver, CO 80241 or E-mail your resume and salary history to: career@auto-trol.com If you have questions on the positions and would like to discuss these, contact Chris Copello at (303) 252-2247. ------------------------------ From: Francoise Chatelin Date: Tue, 16 Apr 1996 15:43:08 +0200 Subject: European Community Research Training Grant European Community Research Training Grant (Post-Graduate level) CERFACS is looking for a post-graduate student to jointly submit an application for a European Community Research Grant (TMR programme). We are looking for a graduate student with experience, interest and background in mathematics and computers, to work on a Ph.D. thesis on eigensolvers (in connection with evolution equations and computation of exponentials). The work will be carried out in the Parallel Algorithms Project (Qualitative Computing Group) at CERFACS, in cooperation with the Aladin project at INRIA/IRISA, under the supervision of Francoise Chatelin and Bernard Philippe. Eligible candidates are non-French citizens from the European Community (+ Iceland, Liechtenstein and Norway). Students interested by this joint application should send relevant information (CV + name of referees + motivation letter) to Valerie Fraysse (fraysse@cerfacs.fr) by May 15th at the latest. More information is available upon request. For detailed information about CERFACS and the Parallel Algorithms Project URL address: http://www.cerfacs.fr/algor For detailed information about the Qualitative Computing Group URL address: http://www.cerfacs.fr/~toumazou/Qualitative.html For detailed information about INRIA/IRISA URL address: http://www.inria.fr/Equipes/ALADIN-eng.html For more information about Toulouse, the city where CERFACS is located URL address: http://www.cict.fr/toulouse/EBienvenue.html ------------------------------ From: Mike Osborne Date: Wed, 17 Apr 1996 12:44:15 +1100 Subject: Positions at Australian National University THE AUSTRALIAN NATIONAL UNIVERSITY SCHOOL OF MATHEMATICAL SCIENCES RESEARCH FELLOW (LEVEL B) FELLOW (LEVEL C) POSITIONS IN MATHEMATICAL SOFTWARE RESEARCH AND DEVELOPMENT The Australian National University and Fujitsu Limited, the world's second largest computer manufacturer, are collaborating in developing numerical algorithms and software in a parallel vector environment for new generation parallel supercomputers such as the VPP700 with a peak speed of 560 Gflops, and the VPP300. Mathematicians or computer scientists with experience in algorithm and software development are sought to join this project (two positions are anticipated). This is an exciting opportunity to contribute to the development of software for some of the most powerful supercomputers of the decade. The appointee will be under the direction of staff from the School of Mathematical Sciences and the Computer Sciences Laboratory, RSISE. Appointees will be expected to interact closely with these groups which are also engaged in the development of algorithms and software for the experimental multi-processor AP1000 supercomputer. We are seeking candidates with a strong background in computational mathematics, experience in parallel and/or vector processing, and demonstrated skills in developing numerical algorithms and implementing them in practice. The successful candidates will be required to develop software and undertake research in some of the following areas: numerical linear algebra, numerical solution of ordinary and partial differential equations, mathematical programming, numerical approximations, signal processing. Current projects include methods for large scale eigenvalue problems, direct and iterative methods for sparse linear systems, development of multigrid preconditioners, and extensions to Fourier transforms and wavelet libraries. Experience in software development for parallel and/or vector computers is desirable. The ability to complete projects on schedule is essential. It is important that candidates be able to take up the post at an early date. An initial appointment of between one and three years will be negotiated. Extension of the appointment may be possible, but will depend on continuing collaborative arrangements with Fujitsu. Persons wishing to take the post on secondment from other positions are encouraged to apply. The ANU has assembled one of the most powerful and broadly-based advanced computing environments to be found in a university. Resources at the ANU include a 28 Gflop Fujitsu VPP300, a 128 processor Fujitsu AP1000, and a 16 node Viking Sparc processor AP+, shortly to be upgraded to 32 nodes. The level of appointment, depending on the candidate's experience and qualifications, will lie within the following salary ranges: Research Fellow [Level B] \$43,042 - \$51,113 p.a. Research Fellow [Level C] \$52,726 - \$60,797 p.a. Further information is available from Dr R Gingold, Supercomputer Facility, phone: (06) 249 3437, Fax (06) 279 8199, and email bob.gingold@anu.edu.au or Professor M Osborne, email mike@thrain.anu.edu.au or Professor R Brent, email rpb@cs.anu.edu.au. Please obtain the further particulars and selection criteria before applying, from the Executive Officer, SMS, phone (61 6) 249 2957, Fax (61 6) 249 0759, E-Mail: Delia.Ritherdon@.anu.edu.au, or from WWW: URL http://anusf.anu.edu.au/~rag900/math Closing Date: 31 May 1996 Ref: SMS 16.4.1 Email addresses and/or fax numbers should be provided for referees so that appointment procedures can be expedited. APPLICATIONS addressing the selection criteria should be submitted in duplicate to The Secretary, The Australian National University, Canberra, ACT 0200 quoting reference number and including curriculum vitae, list of publications and names and addresses of at least three referees. Further information is available from either of the contacts listed above. The University has a "no smoking" policy effective in all University buildings and vehicles. THE UNIVERSITY IS AN EQUAL OPPORTUNITY EMPLOYER ------------------------------ From: Horst Simon Date: Thu, 18 Apr 1996 08:36:27 -0700 Subject: Hans Lewy Postdoctoral Fellowship at LBNL Applications are invited for the Hans Lewy Postdoctoral Fellowship in the Computing Sciences Directorate at the Lawrence Berkeley National Laboratory for 1996-97. The fellowship, which was initiated in 1989, is intended to enhance scientific research in the U.S.A. by sponsoring a recent Ph.D. to work in areas related to scientific computing and numerical algorithms, including the interaction of applications with high performance architectures. Of particular interest are those areas in which the National Energy Research Scientific Computing (NERSC) Division, the Center of Computational Science and Engineering (CCSE), and the LBNL Mathematics Department are active. Among these areas are computational mathematics, turbulence theory, material sciences, interface methods, fluid mechanics, adaptive grid methods, iterative methods, numerical linear algebra, and tools for parallel processing. NERSC will provide access to a 512 processor Cray T3E, and there will be opportunities to interact with the Mathematics faculty and Computer Science faculty at the nearby University of California, Berkeley. (for more information see http://www.lbl.gov/NERSC/ on the WWW). Interested applicants should send a curriculum vitae and names of three references before May 15, 1996 to Lawrence Berkeley Laboratory, Computing Sciences, MS 50B-4230, University of California, Berkeley, CA 94720 to the attention of Michelle Gachis or e-mail to magachis@lbl.gov The fellowship is for one year, beginning in summer or fall of 1996, with possibility of renewal for a second year. The Berkeley Laboratory is an Equal Opportunity employer committed to the development of a diverse workforce. ------------------------------ From: SIAM Date: Mon, 15 Apr 96 12:28:57 EST Subject: Contents, SIAM Optimization SIAM Journal on Optimization MAY 1996, Volume 6, Number 2 CONTENTS A Unified Analysis of Hoffman's Bound Via Fenchel Duality James V. Burke and Paul Tseng A Linesearch Procedure in Barrier Methods for Some Convex Programming Problems A. Melman Differentiable Piecewise Quadratic Exact Penalty Functions for Quadratic Programs With Simple Bound Constraints Wu Li Convergence of an Infeasible Interior-Point Algorithm from Arbitrary Positive Starting Points Stephen C. Billups and Michael C. Ferris Global Convergence Properties of Some Iterative Methods for Linear Complementarity Problems Christian Kanzow An Interior-Point Method for Semidefinite Programming Christoph Helmberg, Franz Rendl, Robert J. Vanderbei, and Henry Wolkowicz Complete Characterizations of Global Optimality for Problems Involving the Pointwise Minimum of Sublinear Functions B. M. Glover, Y. Ishizuka, V. Jeyakumar, and H. D. Tuan Projected Sequential Quadratic Programming Methods Matthias Heinkenschloss An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds Thomas F. Coleman and Yuying Li Equivalence of Complementarity Problems to Differentiable Minimization: A Unified Approach Paul Tseng, Nobuo Yamashita, and Masao Fukushima An SQP Algorithm for Finely Discretized Continuous Minimax Problems and Other Minimax Problems With Many Objective Functions Jian L. Zhou and Andre L. Tits A Parallel Method for Unconstrained Discrete-Time Optimal Control Problems Daniel Ralph A Global Search Method for Discrete Stochastic Optimization Sigrun Andradottir Lipschitz Stability for Stochastic Programs With Complete Recourse Werner Romisch and Rudiger Schultz ------------------------------ End of NA Digest ************************** -------