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© 2020

Linear Programming

Foundations and Extensions

Textbook

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 285)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Part I

    1. Front Matter
      Pages 1-2
    2. Robert J. Vanderbei
      Pages 3-10
    3. Robert J. Vanderbei
      Pages 11-25
    4. Robert J. Vanderbei
      Pages 27-42
    5. Robert J. Vanderbei
      Pages 43-58
    6. Robert J. Vanderbei
      Pages 59-88
    7. Robert J. Vanderbei
      Pages 89-108
    8. Robert J. Vanderbei
      Pages 109-121
    9. Robert J. Vanderbei
      Pages 123-147
    10. Robert J. Vanderbei
      Pages 149-158
    11. Robert J. Vanderbei
      Pages 159-169
    12. Robert J. Vanderbei
      Pages 171-185
    13. Robert J. Vanderbei
      Pages 187-213
    14. Robert J. Vanderbei
      Pages 215-226
  3. Part II

    1. Front Matter
      Pages 227-228
    2. Robert J. Vanderbei
      Pages 229-256
    3. Robert J. Vanderbei
      Pages 257-273
    4. Robert J. Vanderbei
      Pages 275-291
  4. Part III

    1. Front Matter
      Pages 293-294

About this book

Introduction

The book provides a broad introduction to both the theory and the application of optimization with a special emphasis on the elegance, importance, and usefulness of the parametric self-dual simplex method. The book assumes that a problem in “standard form,” is a problem with inequality constraints and nonnegative variables. The main new innovation to the book is the use of clickable links to the (newly updated) online app to help students do the trivial but tedious arithmetic when solving optimization problems.

The latest edition now includes: a discussion of modern Machine Learning applications, as motivational material; a section explaining Gomory Cuts and an application of integer programming to solve Sudoku problems. 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, the primal-dual simplex method, the path-following interior-point method, and and the homogeneous self-dual method. In addition, the author provides online tools that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and online pivot tools can be found on the book's website. The website also includes new online instructional tools and exercises.

Keywords

Linear Programming Mathematical Programming Integer Programming Optimization Models Simplex Method 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 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.

Bibliographic information

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