Theory of Linear and Integer Programming

Alexander Schrijver (Author)

9780471982326, Wiley

Paperback / softback, published 27 April 1998

484 pages
23.8 x 15.6 x 2.7 cm, 0.709 kg

"...a comprehensive exposition of the theory of linear and integer programming...complementing the more practically oriented books." (Zentralblatt MATH, Vol. 970, 2001/20)

Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.

Introduction and Preliminaries.

Problems, Algorithms, and Complexity.

LINEAR ALGEBRA.

Linear Algebra and Complexity.

LATTICES AND LINEAR DIOPHANTINE EQUATIONS.

Theory of Lattices and Linear Diophantine Equations.

Algorithms for Linear Diophantine Equations.

Diophantine Approximation and Basis Reduction.

POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING.

Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming.

The Structure of Polyhedra.

Polarity, and Blocking and Anti-Blocking Polyhedra.

Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming.

The Simplex Method.

Primal-Dual, Elimination, and Relaxation Methods.

Khachiyan's Method for Linear Programming.

The Ellipsoid Method for Polyhedra More Generally.

Further Polynomiality Results in Linear Programming.

INTEGER LINEAR PROGRAMMING.

Introduction to Integer Linear Programming.

Estimates in Integer Linear Programming.

The Complexity of Integer Linear Programming.

Totally Unimodular Matrices: Fundamental Properties and Examples.

Recognizing Total Unimodularity.

Further Theory Related to Total Unimodularity.

Integral Polyhedra and Total Dual Integrality.

Cutting Planes.

Further Methods in Integer Linear Programming.

References.

Indexes.

Subject Areas: Mathematics [PB]