Linear Programming 2 Theory and Extensions

Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method; interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will find this volume of particular interest.

Geometry of Linear Inequality Systems & 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 Thegrams.- Generalized Upper Bounds.- Decomposition of Large-Scale Systems.- Stochastic Programming: Introduction.- Two-Stage Stochastic Programs.