Nemhauser G.L., Wolsey L.A. Integer and Combinatorial Optimization

John Wiley & Sons, Inc., 1999. — xiv, 766 p. — (Wiley-Interscience series in discrete mathematics and optimization). — ISBN 0-471-82819-X, 0-471-35943-2, 978-0-471-35943-2.This book is about the mathematics of discrete optimization, which includes the representation of problems by mathematical models and, especially, the solution of the models. The focus is on understanding the mathematical underpinnings of the algorithms that make it possible to solve (exactly or approximately) the large and complex models that arise in practical applications.
Notes appear at the end of each chapter. Their purpose is to reference our source materials, and to comment briefly on extensions and related topics that are not discussed in the body of the text. The citations and references are selective.
The book can be used as a graduate text or for self-guided reading in several ways. Since we cannot imagine a reader who would want to undertake a straight cover-to-cover reading and since our experience has shown that it is not possible to cover the whole book in even a two-semester, graduate level course, it is necessary to be selective in a first reading.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
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