Ebook: 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.

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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.

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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.
Content:
Front Matter....Pages i-xxv
Geometry of Linear Inequality Systems & the Simplex Method....Pages 1-41
Duality and Theorems of the Alternatives....Pages 43-65
Early Interior-Point Methods....Pages 67-122
Interior-Point Methods....Pages 123-147
Degeneracy....Pages 149-171
Variants of the Simplex Method....Pages 173-206
Transportation Problem and Variations....Pages 207-229
Network Flow Thegrams....Pages 231-250
Generalized Upper Bounds....Pages 251-264
Decomposition of Large-Scale Systems....Pages 265-321
Stochastic Programming: Introduction....Pages 323-333
Two-Stage Stochastic Programs....Pages 335-366
Back Matter....Pages 367-448

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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.
Content:
Front Matter....Pages i-xxv
Geometry of Linear Inequality Systems & the Simplex Method....Pages 1-41
Duality and Theorems of the Alternatives....Pages 43-65
Early Interior-Point Methods....Pages 67-122
Interior-Point Methods....Pages 123-147
Degeneracy....Pages 149-171
Variants of the Simplex Method....Pages 173-206
Transportation Problem and Variations....Pages 207-229
Network Flow Thegrams....Pages 231-250
Generalized Upper Bounds....Pages 251-264
Decomposition of Large-Scale Systems....Pages 265-321
Stochastic Programming: Introduction....Pages 323-333
Two-Stage Stochastic Programs....Pages 335-366
Back Matter....Pages 367-448
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