Linear and Integer Programming vs Linear Integration and Counting

Jean-Bernard Lasserre

ISBN 10: 1441918531 / ISBN 13: 9781441918536

Published by Springer New York, Springer US Dez 2010, 2010

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 184 pp. Englisch.

Seller Inventory # 9781441918536

Bibliographic Details

• Title: Linear and Integer Programming vs Linear Integration and Counting
• Publisher: Springer New York, Springer US Dez 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 1441918531
• ISBN 13: 9781441918536
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 11D millimeters 254 millimeters width by 178 millimeters height by 11 millimeters depth
• Weight: 358 grams

About this title

Synopsis

This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The book provides some new insights on duality concepts for integer programs.

From the Back Cover

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.