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This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.
| Foreword | |
| Preface | |
| Linear Programs | p. 1 |
| Introduction | p. 3 |
| Sample Linear Programs | p. 7 |
| A Production Problem | p. 7 |
| A Diet Problem | p. 14 |
| A Transportation Problem | p. 20 |
| An Informal Algorithm | p. 26 |
| Graphical Representation | p. 28 |
| Tableau Algebra | p. 43 |
| Tableaux and the Duality Equation | p. 43 |
| Pivot Exchange, Row Equations | p. 48 |
| Pivot Exchange, Column Equations | p. 56 |
| Equivalent Tableaux | p. 62 |
| Basic Solutions | p. 67 |
| Inversion | p. 73 |
| Block Pivots | p. 81 |
| Expanded Tableaux | p. 85 |
| Canonical Duality | p. 95 |
| Canonical Dual Linear Programs | p. 95 |
| Sufficient Conditions for Optimality | p. 99 |
| Economic Interpretation of Duality | p. 102 |
| Heuristic Pivoting | p. 111 |
| Optimal Solutions - Unique, Multiple, None | p. 115 |
| The Geometric Picture | p. 120 |
| Feasibility Algorithm | p. 125 |
| Priority Pivoting | p. 132 |
| The Simplex Algorithm | p. 145 |
| The Simplex Algorithm | p. 145 |
| Degeneracy and Cycling | p. 152 |
| Bland's Anticycling Rule | p. 156 |
| Theorems of the Two Alternatives | p. 161 |
| The Dual Simplex Algorithm | p. 163 |
| The Theorem of the Four Alternatives | p. 166 |
| The Existence-Duality Theorem | p. 170 |
| General Linear Programs | p. 177 |
| General Dual Linear Programs | p. 177 |
| Reduction to Canonical Form | p. 181 |
| The Two-Phase Simplex Method | p. 185 |
| Systems of Linear Inequalities | p. 190 |
| Complementary Slackness | p. 198 |
| Numerical Considerations | p. 209 |
| Numerical Considerations | p. 209 |
| The Revised Simplex Method | p. 213 |
| Gaussian Elimination | p. 221 |
| Numerical Accuracy | p. 229 |
| The Ellipsoidal Algorithm | p. 239 |
| The Karmarkar Algorithm | p. 241 |
| Related Problems | p. 251 |
| Matrix Games | p. 253 |
| Matching Games | p. 253 |
| Optimal Strategies | p. 258 |
| Matrix Games and Linear Programs | p. 261 |
| Linear Programs and Symmetric Games | p. 267 |
| Assignment and Matching Problems | p. 275 |
| The Assignment Problem | p. 275 |
| Kuhn's Hungarian Algorithm | p. 280 |
| Konig's Theorem | p. 284 |
| Matching and Hall's Theorem | p. 293 |
| Assignments and Linear Programs | p. 298 |
| Egervary's Theorem | p. 305 |
| Von Neumann's Hide-and-Seek Game | p. 307 |
| Doubly Stochastic Matrices | p. 310 |
| The Transportation Problem | p. 319 |
| The Transportation Problem | p. 319 |
| Phase One of Dantzig's Method | p. 324 |
| The Dual of the Transportation Problem | p. 332 |
| Dantzig's Method | p. 338 |
| Economic Interpretation of the Dual Program | p. 345 |
| Graphs and Trees | p. 349 |
| Structure of Network Problems | p. 354 |
| Pivoting in Graphs | p. 359 |
| Network Flow Problems | p. 373 |
| Network Flow Problems | p. 373 |
| The Ford-Fulkerson Algorithm | p. 379 |
| The Max-Flow, Min-Cut Theorem | p. 385 |
| The Transshipment Problem | p. 395 |
| The Transshipment Problem | p. 395 |
| Shortest Path Problems | p. 400 |
| A Transshipment Algorithm | p. 408 |
| Nonlinear Programs | p. 419 |
| Karush-Kuhn-Tucker Theorem | p. 419 |
| The Constraint Qualification | p. 427 |
| Least Squares | p. 433 |
| Least Distance | p. 439 |
| Hybrid Problems | p. 444 |
| Empirical Principal Pivoting | p. 450 |
| Quadratic Programs | p. 455 |
| Semidefinite Quadratic Programs | p. 461 |
| An Algorithm for Quadratic Programs | p. 468 |
| Noncanonical Quadratic Programs | p. 481 |
| A Answers | p. 493 |
| Selected Bibliography | p. 575 |
| Index | p. 579 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
ISBN: 9780125154406
ISBN-10: 0125154402
Series: Computer Science & Scientific Computing
Audience:
Tertiary; University or College
Format:
Hardcover
Language:
English
Number Of Pages: 584
Published: 1st October 1992
Publisher: ACADEMIC PR INC
Country of Publication: US
Dimensions (cm): 23.7 x 16.23
x 3.33
Weight (kg): 1.04
