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    The Bone Clocks

    David Mitchell 9781400065677

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Linear and Integer Programming Vs Linear Integration and Counting: A Duality Viewpoint (Springer Series in Operations Research and Financial Enginee)

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Linear and Integer Programming Vs Linear Integration and Counting: A Duality Viewpoint (Springer Series in Operations Research and Financial Enginee) Cover

 

Synopses & Reviews

Publisher Comments:

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.

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.

Table of Contents

Preface. Introduction.- Part I. Linear Integration and Linear Programming. The Linear Integration Problem I. Comparing the Continuous Problems P and I.- Part II. Linear Counting and Integer Programming- The Linear Counting Problem I(d). Relating the Discrete Problems P(d) and I(d) with P.- Part III. Duality. Duality and Gomory Relaxations. Barvinok's Counting Algorithm and Gomory Relaxations. A Discrete Farkas Lemma. The Integer Hull of a Convex Rational Polytope. Duality and Superadditive Functions.- Appendix: Legendre-Fenchel, Laplace, Cramer, and Z Transforms. References. Glossary.- Index.

Product Details

ISBN:
9781441918536
Author:
Lasserre, Jean-bernard
Publisher:
Springer
Author:
Lasserre, Jean-Bernard
Location:
New York, NY
Subject:
Business Writing
Subject:
Operations Research
Subject:
Briâon
Subject:
Vergne
Subject:
interger programming
Subject:
linear integration
Subject:
Linear Programming
Subject:
linear summation
Subject:
Operations Research, Management Science
Subject:
OPTIMIZATION
Subject:
Discrete Mathematics in Computer Science
Subject:
Convex and Discrete Geometry
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Mathematical optimization
Subject:
Computational complexity
Subject:
Discrete groups
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2009
Series:
Springer Series in Operations Research and Financial Engineering
Publication Date:
20101215
Binding:
TRADE PAPER
Language:
English
Pages:
182
Dimensions:
235 x 178 mm 323 gr

Related Subjects

Business » Business Plans
Business » General
Business » Management
Business » Writing
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » General

Linear and Integer Programming Vs Linear Integration and Counting: A Duality Viewpoint (Springer Series in Operations Research and Financial Enginee) New Trade Paper
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Product details 182 pages Springer - English 9781441918536 Reviews:
"Synopsis" by , 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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