ENGLISH

Linear and integer programming vs linear integration and counting: A duality viewpoint

By Jean-Bernard Lasserre (auth.)

Book information

Publisher
Springer-Verlag New York
Year
2009
ISBN
9780387094137, 038709413X
DOI
10.1007/978-0-387-09414-4
Open Library ID
OL4048419M
Language
english
Format
PDF
Filesize
786 kB (804761 bytes)
Series
Springer Series in Operations Research and Financial Engineering
Edition
1
Pages
168\164
Library
Kolxo3
Time added
2009-12-04 00:34:26
Convex and Discrete Geometry; Discrete MathematicsMathematical Programming

Description

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.

Similar books