Linear Programming: Foundations and Extensions

by Robert J Vanderbei

Overview

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.

Product Details

ISBN-13:	9781461476306
Publisher:	Springer-Verlag New York, LLC
Publication date:	07/16/2013
Series:	International Series in Operations Research & Management Science , #196
Sold by:	Barnes & Noble
Format:	eBook
File size:	7 MB

About the Author

Robert J. Vanderbei is Professor of Operations Research and Financial Engineering, and 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

Introduction.- The Simplex Method.- Degeneracy.- Efficiency of the Simplex Method.- Duality Theory.- The Simplex Method in Matrix Notation.- Sensitivity and Parametric Analyses.- Implementation Issues.- Problems in General Form.- Convex Analysis.- Game Theory.- Regression.- Financial Applications.- Network-Type Problems.- Applications.- Structural Optimization.- The Central Path.- A Path-Following Method.- The KKT System.- Implementation Issues.- The Affine-Scaling Method.- The Homogeneous Self-Dual Method.- Integer Programming.- Quadratic Programming.- Convex Programming.

Editorial Reviews

From the reviews of the third edition:

"Robert Vanderbei’s textbook on linear programming, now in its third edition, builds on many of the approaches used by Chvátal and includes up-to-date coverage of a number of topics, including interior point methods, that have become important in the 25 years since the publication of Chvátal’s book. Vanderbei’s book is divided into four parts. … suitable for use in a first course in linear programming covering the simplex method at the advanced undergraduate or graduate level." (Brian Borchers, MathDL, May, 2008)

From the Publisher