Linear programming represents one of the major applications of mathematics to business, industry, and economics. George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. This second volume adds to the theory of the items discussed in the first volume. In addition, it includes advanced topics including variants of the simplex method, interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory.

Klappentext

George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.

Inhalt

Geometry of Linear Inequality Systems and the Simplex Method * Duality and Theorems of the Alternatives * Early Interior-Point Methods * Interior-Point Methods * Degeneracy * Variants of the Simplex Method * Transportation Problem and Variations * Network Flow Theory * Generalized Upper Bounds * Decomposition of Large-Scale Systems * Stochastic Programming: Introduction * Two-Stage Stochastic Programs * Appendix: Probability Theory: Overview