Linear Programs & Related Problems

A Volume in the Computer Science and Scientific Computing Series

By: Evar D. Nering, Albert W. Tucker

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Hardcover | 12 October 1992

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584 Pages

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23.7 x 16.23 x 3.33

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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.

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Non-Fiction Mathematics Optimisation Linear Programming Engineering & Technology Technology in General Maths for Engineers Science Science in General Maths for Scientists Probability & Statistics Computing & I.T.

Computer Science Engineering in General

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.

Linear Programs & Related Problems

A Volume in the Computer Science and Scientific Computing Series

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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