Logic And Integer Programming
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Logic and Integer Programming
Author: H. Paul Williams
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-04-09
Paul Williams, a leading authority on modeling in integer programming, has written a concise, readable introduction to the science and art of using modeling in logic for integer programming. Written for graduate and postgraduate students, as well as academics and practitioners, the book is divided into four chapters that all avoid the typical format of definitions, theorems and proofs and instead introduce concepts and results within the text through examples. References are given at the end of each chapter to the more mathematical papers and texts on the subject, and exercises are included to reinforce and expand on the material in the chapter. Methods of solving with both logic and IP are given and their connections are described. Applications in diverse fields are discussed, and Williams shows how IP models can be expressed as satisfiability problems and solved as such.
Theory of Linear and Integer Programming
Author: Alexander Schrijver
language: en
Publisher: John Wiley & Sons
Release Date: 1998-06-11
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
Logic and Integer Programming
Paul Williams, a leading authority on modeling in integer programming, has written a concise, readable introduction to the science and art of using modeling in logic for integer programming. Written for graduate and postgraduate students, as well as academics and practitioners, the book is divided into four chapters that all avoid the typical format of definitions, theorems and proofs and instead introduce concepts and results within the text through examples. References are given at the end of each chapter to the more mathematical papers and texts on the subject, and exercises are included to reinforce and expand on the material in the chapter. Methods of solving with both logic and IP are given and their connections are described. Applications in diverse fields are discussed, and Williams shows how IP models can be expressed as satisfiability problems and solved as such.