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Description of  Theory of Linear and Integer Programming

Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. 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. Contents 1 Introduction and preliminaries 2 Problems, algorithms, and complexity 3 Linear algebra and complexity 4 Theory of lattices and linear diophantine equations 5 Algorithms for linear diophantine equations 6 Diophantine approximation and basis reduction 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming 8 The structure of polyhedra 9 Polarity, and blocking and anti-blocking polyhedra 10 Sizes and the theoretical complexity of linear inequalities and linear programming 11 The simplex method 12 Primal-dual, elimination, and relaxation methods 13 Khachiyan's method for linear programming 14 The ellipsoid method for polyhedra more generally 15 Further polynomiality results in linear programming 16 Introduction to integer linear programming 17 Estimates in integer linear programming 18 The complexity of integer linear programming 19 Totally unimodular matrices: fundamental properties and examples 20 Recognizing total unimodularity 21 Further theory related to total unimodularity 22 Integral polyhedra and total dual integrality 23 Cutting planes 24 Further methods in integer linear programming Historical and further notes on integer linear programming References Notation index Author index Subject index