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Mathematics - Applications | Linear Programming - Foundations and Extensions

Linear Programming

Foundations and Extensions

Vanderbei, Robert J

2nd ed. 2001, XVIII, 450 p.


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  • 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.




Content Level » Research

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

Related subjects » Applications - Mathematics - Operations Research & Decision Theory - Theoretical Computer Science

Table of contents 

1. Basic Theory—The Simplex Method and Duality.- 1. Introduction.- 2. The Simplex Method.- 3. Degeneracy.- 4. Efficiency of the Simplex Method.- 5. Duality Theory.- 6. The Simplex Method in Matrix Notation.- 7. Sensitivity and Parametric Analyses.- 8. Implementation Issues.- 9. Problems in General Form.- 10. Convex Analysis.- 11. Game Theory.- 12. Regression.- 2. Network-Type Problems.- 13. Network Flow Problems.- 14. Applications.- 15. Structural Optimization.- 3. Interior-Point Methods.- 16. The Central Path.- 17. A Path-Following Method.- 18. The KKT System.- 19. Implementation Issues.- 20. The Affine-Scaling Method.- 21. The Homogeneous Self-Dual Method.- 4. Extensions.- 22. Integer Programming.- 23. Quadratic Programming.- 24. Convex Programming.- Appendix A. Source Listings.- 1. The Self-Dual Simplex Method.- 2. The Homogeneous Self-Dual Method.- Answers to Selected Exercises.

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