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Linear Programming: Methods and Applications

Saul I. Gass
Dover Publications
Publication Date: 
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Allen Stenger
, on

This is a comprehensive textbook in linear programming, slanted toward the difficulties that arise in optimizing large real-life systems. The present volume is a slightly-corrected reprint of the 1985 McGraw-Hill fifth edition.

The book is aimed at a broad mathematics, engineering, and economics audience at the upper undergraduate level. It includes a chapter of fairly detailed background material on the linear mathematics needed. Much of the book deals with algorithmic issues such as finding a first feasible solution, stability, sensitivity, anti-cycling, sparse matrices, and implementation issues for computer programs. It does not cover specific numerical analysis issues such as rounding error. The book covers primarily the simplex method and continuous linear problems, but also has some material on integer programming and on nonlinear programming. It was last updated in 1985 and so does not cover discoveries made since then, such as Khachiyan's algorithm and Karmarkar's algorithm.

Bottom line: a thorough, broadly-applicable, and not-too-dated text at a bargain Dover price.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at, a math help site that fosters inquiry learning.

1. General Discussion
2. Mathematical Background
3. The General Linear-programming Problem
4. The Simplex Computational Procedure
5. The Revised Simplex Method
6. The Duality Problems of Programming
7. Degeneracy Procedures
8. Parametric Linear Programming and Sensitivity
9. Additional Computational Techniques
10. The Transportation Problem
11. General Linear-Programming Applications
12. Nonlinear Programming