{"product_id":"theory-of-linear-and-integer-programming-isbn-9780471982326","title":"Theory of Linear and Integer Programming","description":"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 indexAls Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.  Introduction and Preliminaries.\u003cbr\u003e \u003cbr\u003e Problems, Algorithms, and Complexity.\u003cbr\u003e \u003cbr\u003e LINEAR ALGEBRA.\u003cbr\u003e \u003cbr\u003e Linear Algebra and Complexity.\u003cbr\u003e \u003cbr\u003e LATTICES AND LINEAR DIOPHANTINE EQUATIONS.\u003cbr\u003e \u003cbr\u003e Theory of Lattices and Linear Diophantine Equations.\u003cbr\u003e \u003cbr\u003e Algorithms for Linear Diophantine Equations.\u003cbr\u003e \u003cbr\u003e Diophantine Approximation and Basis Reduction.\u003cbr\u003e \u003cbr\u003e POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING.\u003cbr\u003e \u003cbr\u003e Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming.\u003cbr\u003e \u003cbr\u003e The Structure of Polyhedra.\u003cbr\u003e \u003cbr\u003e Polarity, and Blocking and Anti-Blocking Polyhedra.\u003cbr\u003e \u003cbr\u003e Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming.\u003cbr\u003e \u003cbr\u003e The Simplex Method.\u003cbr\u003e \u003cbr\u003e Primal-Dual, Elimination, and Relaxation Methods.\u003cbr\u003e \u003cbr\u003e Khachiyan's Method for Linear Programming.\u003cbr\u003e \u003cbr\u003e The Ellipsoid Method for Polyhedra More Generally.\u003cbr\u003e \u003cbr\u003e Further Polynomiality Results in Linear Programming.\u003cbr\u003e \u003cbr\u003e INTEGER LINEAR PROGRAMMING.\u003cbr\u003e \u003cbr\u003e Introduction to Integer Linear Programming.\u003cbr\u003e \u003cbr\u003e Estimates in Integer Linear Programming.\u003cbr\u003e \u003cbr\u003e The Complexity of Integer Linear Programming.\u003cbr\u003e \u003cbr\u003e Totally Unimodular Matrices: Fundamental Properties and Examples.\u003cbr\u003e \u003cbr\u003e Recognizing Total Unimodularity.\u003cbr\u003e \u003cbr\u003e Further Theory Related to Total Unimodularity.\u003cbr\u003e \u003cbr\u003e Integral Polyhedra and Total Dual Integrality.\u003cbr\u003e \u003cbr\u003e Cutting Planes.\u003cbr\u003e \u003cbr\u003e Further Methods in Integer Linear Programming.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Indexes. \"...a comprehensive exposition of the theory of linear and integer programming...complementing the more practically oriented books.\" (Zentralblatt MATH, Vol. 970, 2001\/20) Professor Schrijver has held tenured positions with the Mathematisch Centrum in Amsterdam, and the University of Amsterdam. He has spent leaves of absence in Oxford and Szeged (Hungary). In 1983 he was appointed to the post of Professor of Mathematics at Tilburg University, The Netherlands, with a partial engagement at the Centrum voor Wiskunde en Informatica in Amsterdam. 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","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990381117669,"sku":"NP9780471982326","price":139.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471982326.jpg?v=1761787596","url":"https:\/\/k12savings.com\/products\/theory-of-linear-and-integer-programming-isbn-9780471982326","provider":"K12savings","version":"1.0","type":"link"}