Linear Programming: Foundations and Extensions

by Robert J. Vanderbei

Overview

Linear Programming: Foundations and Extensions, Third Edition is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeds to cover convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written with specific examples and concrete algorithms preceding more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.

Moreover, Linear Programming: Foundations and Extensions, Third Edition underscores the purpose of optimization-to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: The two-phase simplex method, The primal-dual simplex method, The path-following interior-point method, The homogeneous self-dual methods. In addition, there are online JAVA applets which 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 books webpage: http://www.princeton.edu/-rvdb/LPbook/. Also check the book's webpage for new online instructional tools and exercises that have been added in the new edition.

Product Details

ISBN-13:	9780792398042
Publisher:	Springer US
Publication date:	12/31/1996
Series:	International Series in Operations Research & Management Science , #4
Edition description:	1997
Pages:	418
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

About the Author

Robert J. Vanderbei is Professor of Operations Research and Financial Engineering, and former Department Chair, OR and Financial Engineering at Princeton University. His research interests are in algorithms for nonlinear optimization and their application to problems arising in engineering and science. Application areas of interest focus mainly on inverse Fourier transform optimization problems and action minimization problems with a special interest in applying these techniques to the design of NASA’s terrestrial planet finder space telescope.

Table of Contents

Preface. Part 1: Basic Theory - The Simplex Method and Duality. 1. Introduction. 2. The Simplex Method. 3. Degeneracy. 4. Efficiency of the Simplex Method. 5. Duality Theory. 6. The Simplex Method in Matrix Notation. 7. Sensitivity and Parametric Analyses. 8. Implementation Issues. 9. Problems in General Form. 10. Convex Analysis. 11. Game Theory. 12. Regression. Part 2: Network-Type Problems. 13. Network Flow Problems. 14. Applications. 15. Structural Optimization. Part 3: Interior-Point Methods. 16. The Central Path. 17. A Path-Following Method. 18. The KKT System. 19. Implementation Issues. 20. The Affine-Scaling Method. 21. The Homogeneous Self-Dual Method. Part 4: Extensions. 22. Integer Programming. 23. Quadratic Programming. 24. Convex Programming. Appendix A: Source Listings. Answers to Selected Exercises. Bibliography. Index.

Editorial Reviews

Constrained optimization is introduced here with specific examples and concrete algorithms preceding more abstract topics. The book begins with treatment of linear programming, then proceeds to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Dynamic programming and the linear complementarity problem are covered as well. Early chapters assume background only in linear algebra. Later chapters require some knowledge of multivariate calculus. Code is included for C programs that implement example algorithms. This second edition adds many new exercises, and offers online tools for learning the simplex method and duality theory. Vanderbei is affiliated with the Department of Operations Research & Financial Engineering at Princeton University. Annotation c. Book News, Inc., Portland, OR (booknews.com)

A introduction to the subject; the first two sections assume only linear algebra, but the other two require some knowledge of multivariate calculus, particularly the ability to use Lagrange multipliers to solve simple calculus problems in two and three dimensions. Includes source code in C for five of the problems discussed, and answers to some of the exercises. Annotation c. by Book News, Inc., Portland, Or.

Booknews

‘Vanderbei's book is thoroughly modern. Vanderbei's book has many novel features. Some nice features. This book has style. Overall, I greatly enjoyed reviewing this book, and I highly recommend it as a textbook for an advanced undergraduate or master's level course in linear programming, particularly for courses in an engineering environment. In addition, it also is a good reference book for interior point methods as well as for implementation and computational aspects of linear programming. This is an excellent new book.'
Robert Freund, (MIT) in Optima, 56 (1997)
‘In conclusion, Vanderbei's book gives an excellent introduction to linear programminbg, especially the algorithmic side of the subject. The book is highly recommended for both self study and as teaching material.'
Optima, 58 (1998)

From the Publisher