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Continued from the back cover: "A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies.
"The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians."
BRIEF CONTENTS
Introduction and preliminaries
Problems, algorithms, and complexity
Part I. Linear Algebra
Linear algebra and complexity
Part II. Lattices and Linear Diophantine Equations
Theory of lattices and linear diophantine equations
Algorithms for linear diophantine equations
Diophantine approximation and basis reduction
Part III. 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
Part IV. 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
The book concludes with References, Notation Index, Author Index, and Subject Index.
