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Linear and Integer Programming vs Linear Integration and Counting: A Duality Viewpoint (Springer Series in Operations Research and Financial Engineering) - Tapa blanda

Libro 14 de 43: Springer Series in Operations Research and Financial Engineering

Lasserre, Jean-Bernard

 
9781441918536: Linear and Integer Programming vs Linear Integration and Counting: A Duality Viewpoint (Springer Series in Operations Research and Financial Engineering)
Tapa blanda
ISBN 10: 1441918531 ISBN 13: 9781441918536
Editorial: Springer, 2010

Sinopsis

Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.

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De la contraportada

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
1441918531
ISBN 13 
9781441918536
Encuadernación
Tapa blanda
Número de páginas
168
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

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