Integer Programming

ISBN-13: 9783319110073 / Angielski / Twarda / 2014 / 456 str.

Michele Conforti;Gérard Cornuéjols;Giacomo Zambelli

Opis

This book is an elegant and rigorous presentation of integer programming, exposing the subject's mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader's understanding and serving as a gateway to deeper study. Key topics include: * formulations* polyhedral theory* cutting planes* decomposition* enumeration* semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.

Recenzje

"Integer Programming begins by introducing the subject and giving several examples of integer programming problems. ... This book would be suitable for a graduate level course on the mathematics of cutting plane methods. ... This book might also be of interest as a reference for researchers working in this area. ... This book offers a more focused presentation that makes it better suited for use as a textbook." (Brian Borchers, MAA Reviews, maa.org, December, 2015)

"The book is written in a very clear and didactic style. ... very useful for mathematically mature undergraduates, graduate students, postdocs, and established researchers who are interested in the techniques. ...This is an excellent and impressive book. We wholeheartedly recommend it as a textbook for advanced undergraduate and introductory graduate courses on integer programming." (Jakub Marecek, Interfaces, Vol. 45 (5), September-October, 2015)

"The authors deliver a comprehensive presentation of integer programming. ... Everything is presented in a rigorous way, but on the other hand, the form makes it easy to understand for everyone. Each chapter is followed by the exercises, that allow to recall the contents. ... the book is an essential text in the field of integer programing, that should be recommended as a very useful textbook for students, but also a valuable introduction for the researchers in this area." (Marcin Anholcer, zbMATH 1307.90001, 2015)

Spis treści

Preface.- 1 Getting Started.- 2 Integer Programming Models.- 3 Linear Inequalities and Polyhedra.- 4 Perfect Formulations.- 5 Split and Gomory Inequalities.- 6 Intersection Cuts and Corner Polyhedra.- 7 Valid Inequalities for Structured Integer Programs.- 8 Reformulations and Relaxations.- 9 Enumeration.- 10 Semidefinite Bounds.- Bibliography.- Index.

O autorze

Michelangelo Conforti is Professor of Mathematics at the University of Padova. Together with G. Cornuéjols and M. R. Rao, he received the 2000 Fulkerson Prize in discrete mathematics.

Gérard Cornuéjols is IBM University Professor of Operations Research at Carnegie Mellon University. His research has been recognized by numerous honors, among them the Fulkerson Prize, the Frederick W. Lanchester Prize, the Dantzig Prize, and the John von Neumann Theory Prize.

Giacomo Zambelli is Associate Professor (Reader) of Management Science at the London School of Economics and Political Sciences.

All three authors are leading experts in the fields of integer programming, graph theory, and combinatorial optimization.