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Linear and Integer Programming Vs Linear Integration and Counting: A Duality Viewpoint

Jean B. Lasserre

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ISBN 10: 1441918531 / ISBN 13: 9781441918536
Published by Springer-Verlag New York Inc.
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168 pages. Dimensions: 9.8in. x 7.0in. x 0.5in.Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely efcient 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) min213x1928x11111x2345x 9123x 1 2 3 4 5 s. t. 12223x 12224x 36674x 61119x 85569x 89643482, 1 2 3 4 5 x , x , x , x , xN, 1 2 3 4 5 taken from a list of difcult knapsack problems in Aardal and Lenstra 2, is not solved even by hours of computing, using for instance the last version of the efcient 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9781441918536

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Bibliographic Details

Title: Linear and Integer Programming Vs Linear ...

Publisher: Springer-Verlag New York Inc.

Binding: Paperback

Book Condition:New

Book Type: Paperback

About this title


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.

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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.

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