Integer and Combinatorial Optimization

ISBN-13: 9780471359432 / Angielski / Miękka / 1999 / 784 str.

Laurence A. Wolsey; George L. Nemhauser

Opis

Written by international experts in the field of integer programming, this text and reference presents the mathematical foundations, theory, and algorithms of discrete optimization methods, incorporating many techniques as well as numerous examples and model formulations. Throughout, the notation used is clear and consistent and the level of mathematics never becomes excessive: difficult theorems are approached via a series of propositions, and proofs accurately reference the earlier results at each stage.

Spis treści

FOUNDATIONS.

The Scope of Integer and Combinatorial Optimization.

Linear Programming.

Graphs and Networks.

Polyhedral Theory.

Computational Complexity.

Polynomial–Time Algorithms for Linear Programming.

Integer Lattices.

GENERAL INTEGER PROGRAMMING.

The Theory of Valid Inequalities.

Strong Valid Inequalities and Facets for Structured Integer Programs.

Duality and Relaxation.

General Algorithms.

Special–Purpose Algorithms.

Applications of Special– Purpose Algorithms.

COMBINATORIAL OPTIMIZATION.

Integral Polyhedra.

Matching.

Matroid and Submodular Function Optimization.

References.

Indexes.

Blurb

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION

"This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."–Optima

"A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."–Computing Reviews

"[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."–Mathematical Reviews

"This comprehensive and wide–ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."–Bulletin of the London Mathematical Society

"This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."–Times Higher Education Supplement, London

Also of interest . . .

INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self–contained, this intermediate–level guide to integer programming provides readers with clear, up–to–date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0–471–28366–5) 260 pp.