Linear Programming: Foundations and Extensions

✍ Scribed by Robert J Vanderbei (auth.)

• Publisher: Springer US
• Year: 2014
• Tongue: English
• Leaves: 421
• Series: International Series in Operations Research & Management Science 196
• Edition: 4
• Category: Library

✦ Synopsis

This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications.

Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.

✦ Table of Contents

Front Matter....Pages i-xxii
Front Matter....Pages 1-2
Introduction....Pages 3-9
The Simplex Method....Pages 11-23
Degeneracy....Pages 25-37
Efficiency of the Simplex Method....Pages 39-52
Duality Theory....Pages 53-79
The Simplex Method in Matrix Notation....Pages 81-97
Sensitivity and Parametric Analyses....Pages 99-109
Implementation Issues....Pages 111-132
Problems in General Form....Pages 133-140
Convex Analysis....Pages 141-150
Game Theory....Pages 151-163
Regression....Pages 165-184
Financial Applications....Pages 185-195
Front Matter....Pages 197-198
Network Flow Problems....Pages 199-224
Applications....Pages 225-239
Structural Optimization....Pages 241-254
Front Matter....Pages 255-256
The Central Path....Pages 257-268
A Path-Following Method....Pages 269-283
The KKT System....Pages 285-291
Implementation Issues for Interior-Point Methods....Pages 293-307
Front Matter....Pages 255-256
The Affine-Scaling Method....Pages 309-321
The Homogeneous Self-Dual Method....Pages 323-341
Front Matter....Pages 343-344
Integer Programming....Pages 345-362
Quadratic Programming....Pages 363-378
Convex Programming....Pages 379-388
Back Matter....Pages 389-414

✦ Subjects

Operation Research/Decision Theory; Operations Research, Management Science; Optimization