Springer Series in Operations Research and Financial Engineering

Linear and Integer Programming vs Linear Integration and Counting

A Duality Viewpoint

Authors: Lasserre, Jean B.

  • Analyzes and compares four closely related nontrivial problems, namely linear programming, integer programming, linear integration, linear summation (or counting) with a focus on duality
  • Provides some new insights on duality concepts for integer programs, and also permits to retrieve and shed new light on some well-known results
see more benefits

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-0-387-09414-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-0-387-09413-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4419-1853-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

From the reviews:

“Lasserre has produced a fascinating slim … monograph (much of the work his own) looking at the parallels between linear (respectively integer) programming on the one hand and integration (respectively integer counting) problems on the other hand. … An appendix on various transforms a hundred references and a brief index complete the work which is a welcome addition to an important set of topics.” (J. Borwein, Mathematical Reviews, Issue 2010 f)

“This book is devoted to analysing four important problems: integer programming problem, linear programming problem, linear integration problem, and linear counting problem. … a very specialized book on the integer programming problem and its dual variants. … can be very helpful for researchers working in developing algorithms for the integer programming problem which is a formidable challenging problem. This is a clear and well-written book … .” (E. Almehdawe, Journal of the Operational Research Society, Vol. 61 (12), 2010)


Table of contents (10 chapters)

  • Introduction

    Lasserre, Jean-Bemard

    Pages 1-5

  • The Linear Integration Problem I

    Lasserre, Jean-Bemard

    Pages 9-29

  • Comparing the Continuous Problems P and I

    Lasserre, Jean-Bemard

    Pages 31-37

  • The Linear Counting Problem Id

    Lasserre, Jean-Bemard

    Pages 41-69

  • Relating the Discrete Problems Pd and Id with P

    Lasserre, Jean-Bemard

    Pages 71-79

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-0-387-09414-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-0-387-09413-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4419-1853-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Linear and Integer Programming vs Linear Integration and Counting
Book Subtitle
A Duality Viewpoint
Authors
Series Title
Springer Series in Operations Research and Financial Engineering
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-09414-4
DOI
10.1007/978-0-387-09414-4
Hardcover ISBN
978-0-387-09413-7
Softcover ISBN
978-1-4419-1853-6
Series ISSN
1431-8598
Edition Number
1
Number of Pages
XIV, 168
Number of Illustrations and Tables
2 b/w illustrations
Topics