# Optimization Over Integers

## Dimitris Bertsimas; Robert Weismantel

Note moyenne 4,5
( 2 avis fournis par Goodreads )

The book provides a unified, insightful, and modern treatment of the theory of integer optimization.

The book is used in the doctoral level course, "Integer and Combinatorial Optimization" at the Massachusetts Institute of Technology.

The chapters of the book are logically organized in four parts:

Part I: Formulations and relaxations includes Chapters 1-5 and discusses how to formulate integer optimization problems, how to enhance the formulations to improve the quality of relaxations, how to obtain ideal formulations, the duality of integer optimization and how to solve the resulting relaxations both practically and theoretically.

Part II: Algebra and geometry of integer optimization includes Chapters 6-8 and develops the theory of lattices, oulines ideas from algebraic geometry that have had an impact on integer optimization, and most importantly discusses the geometry of integer optimization, a key feature of the book. These chapters provide the building blocks for developing algorithms.

Part III: Algorithms for integer optimization includes Chapters 9-12 and develops cutting plane methods, integral basis methods, enumerative and heuristic methods and approximation algorithms. The key characteristic of our treatment is that our development of the algorithms is naturally based on the algebraic and geometric developments of Part II.

Part IV: Extensions of integer optimization includes Chapters 13 and 14, and treats mixed integer optimization and robust discrete optimization. Both areas are practically significant as real world problems have very often both continuous and discrete variables and have elements of uncertainty that need to be addressed in a tractable manner.

Distinguishing Characteristics Of This Book:

* Develops the theory of integer optimization from a new geometric perspective via integral generating sets;

* Emphasizes strong formulations, ways to improve them, integral polyhedra, duality, and relaxations;

* Discusses applications of lattices and algebraic geometry to integer optimization, including Grobner bases, optimization over polynomials and counting integer points in polyhedra;

* Contains a unified geometric treatment of cutting plane and integral basis methods;

* Covers enumerative and heuristic methods, including local search over exponential neighborhoods and simulated annealing;

* Presents the major methods to construct approximation algorithms: primal-dual, randomized rounding, semidefinite and enumerative methods;

* Provides a unified treatment of mixed integer and robust discrete optimization;

* Includes a large number of examples and exercises developed through extensive classroom use.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

From the Author :

The purpose of this book is to provide a unified, insightful, and modern treatment of the theory of integer optimization with an eye towards the future. We have selected those topics that we feel have influenced the current state of the art and most importantly we feel will affect the future of the field. We depart from earlier treatments of integer optimization by placing significant emphasis on strong formulations, duality, algebra and most importantly geometry.

Dimitris Bertsimas is the Codirector of the MIT Operations Research Center. He received his PhD from MIT in 1988, and he has been in the MIT faculty ever since. He is a member of the National Academy of Engineering and area editor of Operations Research . He has received numerous research awards including the Presidential Young Investigator Award, Erlang prize and SIAM's best paper award in optimization.

Robert Weismantel is Professor of Mathematics in the University of Magdeburg, Germany. He received his PhD in 1992 from the University of Berlin, and he has been at the University of Magdeburg since 1998. He has reveived the Gerhard Hess-Prize of the German Science Foundation, and he is associate editor of Mathematical Programming and Discrete Optimization. Since 2004, he is the Coordinator of the European network "Algorithmic Discrete Optimization".

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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## 1.Optimization Over Integers

Edité par Dynamic Ideas (2005)
ISBN 10 : 0975914626 ISBN 13 : 9780975914625
Neuf(s) Couverture rigide Quantité : 2
Vendeur
Murray Media
(North Miami Beach, FL, Etats-Unis)
Evaluation vendeur

Description du livre Dynamic Ideas, 2005. Hardcover. État : New. N° de réf. du libraire P110975914626

Acheter neuf
EUR 161,10
Autre devise
Frais de port : EUR 2,57
Vers Etats-Unis
Destinations, frais et délais

## 2.Optimization Over Integers

Edité par Dynamic Ideas (2005)
ISBN 10 : 0975914626 ISBN 13 : 9780975914625
Neuf(s) Couverture rigide Quantité : 1
Vendeur
Irish Booksellers
(Rumford, ME, Etats-Unis)
Evaluation vendeur

Description du livre Dynamic Ideas, 2005. Hardcover. État : New. book. N° de réf. du libraire 975914626

Acheter neuf
EUR 174,59
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Frais de port : Gratuit
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## 3.Optimization Over Integers

Edité par Dynamic Ideas (2005)
ISBN 10 : 0975914626 ISBN 13 : 9780975914625
Neuf(s) Couverture rigide Quantité : 1
Vendeur
Irish Booksellers
(Rumford, ME, Etats-Unis)
Evaluation vendeur

Description du livre Dynamic Ideas, 2005. Hardcover. État : New. book. N° de réf. du libraire 0975914626

Acheter neuf
EUR 174,59
Autre devise
Frais de port : Gratuit
Vers Etats-Unis
Destinations, frais et délais