Convexity and Optimization in Finite Dimensions I

Name: Convexity and Optimization in Finite Dimensions I
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642462184
Price: 89.58 EUR
Availability: InStock

Автор: Josef Stoer, Christoph Witzgall

Език:

Корици: С меки корици

Издател: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Наличност: Външен склад

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Dantzig's development of linear programming into one of the most applicable optimization techniques...

Информация за книгата

Автор

Josef Stoer, Christoph Witzgall

Език

Английски език

Корици

Книга - С меки корици

Издадена

2012

страници

298

EAN

9783642462184

ISBN

3642462189

Enbook ID

07094463

Издател

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Теглоt

476

Размери

155 x 235 x 17

Пълно описание

Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back ground for the arithmetic of convex optimization to be treated in a sub sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.

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Convexity and Optimization in Finite Dimensions I

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