© 2014

Linear Programming

Foundations and Extensions


Part of the International Series in Operations Research & Management Science book series (ISOR, volume 196)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Basic Theory: The Simplex Method and Duality

    1. Front Matter
      Pages 1-2
    2. Robert J. Vanderbei
      Pages 3-9
    3. Robert J. Vanderbei
      Pages 11-23
    4. Robert J. Vanderbei
      Pages 25-37
    5. Robert J. Vanderbei
      Pages 39-52
    6. Robert J. Vanderbei
      Pages 53-79
    7. Robert J. Vanderbei
      Pages 81-97
    8. Robert J. Vanderbei
      Pages 99-109
    9. Robert J. Vanderbei
      Pages 111-132
    10. Robert J. Vanderbei
      Pages 133-140
    11. Robert J. Vanderbei
      Pages 141-150
    12. Robert J. Vanderbei
      Pages 151-163
    13. Robert J. Vanderbei
      Pages 165-184
    14. Robert J. Vanderbei
      Pages 185-195
  3. Network-Type Problems

    1. Front Matter
      Pages 197-198
    2. Robert J. Vanderbei
      Pages 199-224
    3. Robert J. Vanderbei
      Pages 225-239
    4. Robert J. Vanderbei
      Pages 241-254
  4. Interior-Point Methods

    1. Front Matter
      Pages 255-256

About this book


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.


Linear Programming Mathematical Programming Operations Research Optimization Models Regression Vanderbei

Authors and affiliations

  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

About the authors

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.

Bibliographic information

Industry Sectors
Consumer Packaged Goods
Finance, Business & Banking
Energy, Utilities & Environment


“Technically, this is a graduate text, though it can be taught to seniors. ... One of the things that makes Vanderbei’s book so valuable is that he may be the best writer in his area. His writing is very clear and there is generous use of figures and diagrams. ... A two-book library consisting of Cottle and Thapa [2017] and Vanderbei at the graduate level should cover the needs of any graduate student interested in LP.” (The UMAP Journal, Vol. 41 (1), 2020)