Hu / Robinson Mathematical Programming

Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin, and the U. S. Army at Madison, September 11-13, 1972
1. Auflage 2014
ISBN: 978-1-4832-6079-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 308 Seiten, Web PDF

Mathematical Programming provides information pertinent to the developments in mathematical programming. This book covers a variety of topics, including integer programming, dynamic programming, game theory, nonlinear programming, and combinatorial equivalence. Organized into nine chapters, this book begins with an overview of optimization of very large-scale planning problems that can be achieved on significant problems. This text then introduces non-stationary policies and determines certain operating characteristics of the optimal policy for a very long planning horizon. Other chapters consider the perfect graph theorem by defining some well-known integer-valued functions of an arbitrary graph. This book discusses as well integer programming that deals with the class of mathematical programming problems in which some or all of the variables are required to be integers. The final chapter deals with the basic theorem of game theory. This book is a valuable resource for readers who are interested in mathematical programming. Mathematicians will also find this book useful.

Autoren/Hrsg.

Hu, T. C.

Robinson, Stephen M.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematical Programming;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Chapter 1. On the Need for a System Optimization Laboratory;14
6.1;Need.;14
6.2;Background;16
6.3;Some Examples of Important Applications;17
6.4;The Functions of a Systems Optimization Laboratory;18
6.5;Nature of the Bottleneck;21
6.6;Software Development;22
6.7;External Affairs;23
6.8;Research Projects of a System Optimization Laboratory;23
6.9;REFERENCES;32
7;Chapter 2. A Markov Decision Problem;46
7.1;A Markov Process with Rewards;48
7.2;The policy evaluation equation;55
7.3;Relationship of Linear Programming to Policy Iteration;63
7.4;A Turnpike Theorem;73
7.5;Bibliographic Notes;79
7.6;REFERENCES;79
8;Chapter 3. On the Perfect Graph Theorem;82
8.1;REFERENCES;88
9;Chapter 4. A Survey of Integer Programming Emphasizing Computation and Relations among Models;90
9.1;1. Introduction;91
9.2;2. ILP Models and Some Relationships Among Them;92
9.3;3. Computational Complexity of Integer Programming Problems;112
9.4;4. Enumeration Algorithms;117
9.5;5. Cutting Plane Algorithms;127
9.6;6. Approximate Methods;134
9.7;7. Computational Experience;135
9.8;8. Summary and Synthesis;151
9.9;Acknowledgment;154
9.10;References;155
10;Chapter 5. The Group Problems and Subadditive Functions;170
10.1;1. Introduction;170
10.2;2. Problem Definition;174
10.3;3. Subadditivity for Subgroups U;178
10.4;4. Minimality for Subgroups U;179
10.5;5 · P(G n, u0), u0 . Gn;182
10.6;6. P+(Gn, u0), u0 . l;183
10.7;7. Valid Inequalities for P(U, u0);185
10.8;8. Valid Inequalities for P+(U, u0);185
10.9;9. Rounding Methods;192
10.10;REFERENCES;197
11;Chapter 6. Cyclic Groups, Cutting Planes, Shortest Paths;198
11.1;1. Introduction;198
11.2;2. Algorithm;202
11.3;3. Validity of the Algorithm;205
11.4;4. Cyclic Groups;211
11.5;5. Cutting Planes;216
11.6;6. Shortest Paths;219
11.7;REFERENCES;224
12;Chapter 7. Use of Cyclic Group Methods in Branch and Bound;226
12.1;REFERENCES;239
13;Chapter 8. Simplicial Approximation of an Equilibrium Point for Non-Cooperative N-Person Games;240
13.1;1. Introduction;240
13.2;2. Development of the Method;241
13.3;3. The Standard Triangulation of S;262
13.4;4. Remarks and Observations;268
13.5;5. Some Computed Examples;269
13.6;REFERENCES;272
14;Chapter 9. On Balanced Games without Side Payments;274
14.1;1. Introduction;274
14.2;2. Games and Cores;275
14.3;3. Balanced Sets and Balanced Games;278
14.4;4. An Application to Economics;279
14.5;5. Simplicial Partitions, Sperner's Lemma, and the K-K-M Theorem;282
14.6;7. Generalization of Sperner's Lemma and the K-K-M Theorem;288
14.7;8. Proof of the Scarf-Billera Theorem;291
14.8;9. Some Remarks on Path Following;293
14.9;Appendix. Iterated Barycentric Partitions;297
14.10;REFERENCES;302
15;Index;304