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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.