Linear and Integer Programming vs Linear Integration and Counting: A Duality Viewpoint (Springer Series in Operations Research and Financial Engineering) - Softcover

Lasserre, Jean-Bernard

Softcover

ISBN 10: 1441918531 ISBN 13: 9781441918536

Publisher: Springer, 2010

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.

About this title

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.

Edition details

• Publisher: Springer
• Publication date: 2010
• Language: English
• ISBN 10: 1441918531
• ISBN 13: 9781441918536
• Binding: Paperback
• Number of pages: 182