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Linear Programming

Foundations and Extensions

  • Robert J. Vanderbei

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 37)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Basic Theory—The Simplex Method and Duality

    1. Front Matter
      Pages 1-2
    2. Robert J. Vanderbei
      Pages 3-11
    3. Robert J. Vanderbei
      Pages 13-27
    4. Robert J. Vanderbei
      Pages 29-44
    5. Robert J. Vanderbei
      Pages 45-54
    6. Robert J. Vanderbei
      Pages 55-87
    7. Robert J. Vanderbei
      Pages 89-109
    8. Robert J. Vanderbei
      Pages 111-124
    9. Robert J. Vanderbei
      Pages 125-150
    10. Robert J. Vanderbei
      Pages 151-160
    11. Robert J. Vanderbei
      Pages 161-171
    12. Robert J. Vanderbei
      Pages 173-187
    13. Robert J. Vanderbei
      Pages 189-209
  3. Network-Type Problems

    1. Front Matter
      Pages 211-212
    2. Robert J. Vanderbei
      Pages 213-240
    3. Robert J. Vanderbei
      Pages 241-257
    4. Robert J. Vanderbei
      Pages 259-274
  4. Interior-Point Methods

    1. Front Matter
      Pages 275-276
    2. Robert J. Vanderbei
      Pages 277-289
    3. Robert J. Vanderbei
      Pages 291-306
    4. Robert J. Vanderbei
      Pages 307-313
    5. Robert J. Vanderbei
      Pages 315-331
    6. Robert J. Vanderbei
      Pages 333-347
    7. Robert J. Vanderbei
      Pages 349-369
  5. Extensions

    1. Front Matter
      Pages 371-372
    2. Robert J. Vanderbei
      Pages 373-393
    3. Robert J. Vanderbei
      Pages 395-411
    4. Robert J. Vanderbei
      Pages 413-423
  6. Back Matter
    Pages 425-450

About this book

Introduction

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.

 

 

 

Keywords

Simplex method algorithms convex analysis duality interior-point methods linear optimization linear programming/optimization network flows optimization portfolio optimization programming quadratic programming

Authors and affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Dept. of Operations Research & Financial EngineeringPrinceton UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-5662-3
  • Copyright Information Springer-Verlag US 2001
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-5664-7
  • Online ISBN 978-1-4757-5662-3
  • Series Print ISSN 0884-8289
  • Buy this book on publisher's site
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