another book nnouncement
Forum 'Annonces' - Sujet créé le 2010-01-08 par lasserre
Linear and Integer Programming vs Linear
Integration and Counting
A Duality Viewpoint
J.-B. Lasserre, LAAS-CNRS, Toulouse, France
Springer, New York, 2009.
Springer Series in Operations Research and Financial Engineering
ISBN 978-0-387-09413-7
e-ISBN 978-0-387-09414-4
This book analyzes and compares four closely related problems, namely linear programming,
integer programming, linear integration, and linear summation (or counting). The
focus is on duality and the novel approach 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 which are not very well-known in the optimization community. 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.... more on http://springer.com/978-0-387-09413-7
Integration and Counting
A Duality Viewpoint
J.-B. Lasserre, LAAS-CNRS, Toulouse, France
Springer, New York, 2009.
Springer Series in Operations Research and Financial Engineering
ISBN 978-0-387-09413-7
e-ISBN 978-0-387-09414-4
This book analyzes and compares four closely related problems, namely linear programming,
integer programming, linear integration, and linear summation (or counting). The
focus is on duality and the novel approach 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 which are not very well-known in the optimization community. 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.... more on http://springer.com/978-0-387-09413-7