Overview
- Includes material on traditional business applications (resource allocation, blending, network flows) plus applications from other areas (robust statistics, game theory, optimal design of physical structures, etc.)
- Includes many small fixes throughout the book, as well as a new chapter on financial applications, specifically portfolio optimization and option pricing
- Breaks with tradition and develops the theory based on problems expressed in inequality form rather than the more conventional equality form
- Includes supplementary material: sn.pub/extras
Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 114)
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Table of contents (25 chapters)
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Front Matter
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Basic Theory—The Simplex Method and Duality
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Front Matter
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Network-Type Problems
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Front Matter
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Interior-Point Methods
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Front Matter
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Keywords
About this book
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization.
The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.
Moreover, Linear Programming: Foundations and Extensions 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 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 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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: Linear Programming
Book Subtitle: Foundations and Extensions
Authors: Robert J. Vanderbei
Series Title: International Series in Operations Research & Management Science
DOI: https://doi.org/10.1007/978-0-387-74388-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2008
Series ISSN: 0884-8289
Series E-ISSN: 2214-7934
Edition Number: 3
Number of Pages: XX, 468
Number of Illustrations: 66 b/w illustrations, 16 illustrations in colour
Topics: Operations Research, Management Science, Operations Research/Decision Theory, Optimization, Mathematical Modeling and Industrial Mathematics, Engineering Economics, Organization, Logistics, Marketing, Industrial and Production Engineering