1998 TheoryOfLinearAndIntegerProg

• (Schrijver, 1998) ⇒ Alexander Schrijver. (1998). “Theory of Linear and Integer Programming." Wiley. ISBN:0471982326

Subject Headings: Integer Programming Algorithm, Linear Programming Algorithm, Algorithm Complexity Analysis, Combinatorial Optimization.

Notes

• A references for Linear Diophantine Equations, Diophantine Approximation, Basis Reduction, Polyhedra, Simplex Method, Khachiyan's Method, Ellipsoid Method, Integer Linear Programming, Totally Unimodular Matrix, Unimodular Matrix.

Quotes

Book overview

• 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

16. Introduction to Integer Linear Programming

• In this chapter we describe some introductory theory for integer linear programming.

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
1998 TheoryOfLinearAndIntegerProg	Alexander Schrijver			Theory of Linear and Integer Programming			http://books.google.com/books?id=zEzW5mhppB8C