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＜電子ブック＞
Linear and Integer Programming vs Linear Integration and Counting : A Duality Viewpoint / by Jean-Bernard Lasserre
(Springer Series in Operations Research and Financial Engineering. ISSN:21971773)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIV, 168 p. 2 illus : online resource
著者標目	*Lasserre, Jean-Bernard author SpringerLink (Online service)
件　名	LCSH:Operations research LCSH:Management science LCSH:Mathematical optimization LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Discrete mathematics LCSH:Convex geometry  LCSH:Discrete geometry FREE:Operations Research, Management Science FREE:Optimization FREE:Discrete Mathematics in Computer Science FREE:Convex and Discrete Geometry
一般注記	I Linear Integration and Linear Programming -- The Linear Integration Problem I -- Comparing the Continuous Problems P and I -- II Linear Counting and Integer Programming -- The Linear Counting Problem I -- Relating the Discrete Problems P and I with P -- III Duality -- Duality and Gomory Relaxations -- Barvinok#x2019;s Counting Algorithm and Gomory Relaxations -- A Discrete Farkas Lemma -- The Integer Hull of a Convex Rational Polytope -- Duality and Superadditive Functions In this book the author analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, linear summation (or counting). The focus is on duality and the approach is rather novel as it puts integer programming in perspective with three associated problems, and permits one to define discrete analogues of well-known continuous duality concepts, and the rationale behind them. Also, the approach highlights the difference between the discrete and continuous cases. Central in the analysis are the continuous and discrete Brion and Vergne's formulae for linear integration and counting. This approach provides some new insights on duality concepts for integer programs, and also permits to retrieve and shed new light on some well-known results. For instance, Gomory relaxations and the abstract superadditive dual of integer programs are re-interpreted in this algebraic approach. This book will serve graduate students and researchers in applied mathematics, optimization, operations research and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will also find this book useful HTTP:URL=https://doi.org/10.1007/978-0-387-09414-4

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