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
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"...a comprehensive exposition of the theory of linear and integer programming...complementing the more practically oriented books." (Zentralblatt MATH, Vol. 970, 2001/20)
From the Publisher
Examines the theoretical and polyhedral approach to linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. Describes important recent developments in the field. Applications to combinatorial optimization are given with extensive historical surveys and bibliographies. References.
--This text refers to an out of print or unavailable edition of this title.
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9 of 11 people found the following review helpful:
4.0 out of 5 stars
Advanced LP and IP book,
This review is from: Theory of Linear and Integer Programming (Paperback)
This book is a theoretical book -as said in title. Unless you have solid mathematic background, this book may not be for you. I said "solid" doesn't mean "a lot" or "advanced", just a simple algebra that you learn in high school -but it has to be SOLID :) I use this book in theoretical part of my thesis and dissertation but you can find other substitution though. Look at Integer and Combinatorial Optimization by Nemhauser and Wolsey, it might be more practical.
1 of 1 people found the following review helpful:
5.0 out of 5 stars
Good book,
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This review is from: Theory of Linear and Integer Programming (Paperback)
This book is good. A person with a strong backgroud in mathematics can understand it well, otherwise it will take the reader some time to go through all the details.
7 of 11 people found the following review helpful:
5.0 out of 5 stars
An Eyclopedic reference for linear and integer prog.,
This review is from: Theory of Linear and Integer Programming (Paperback)
A great reference text book, with some great historical notes about the history of both linear and integer programming.It is the first book, both me and my advisor check out, when we require any thing on Linear and Integer Programming.
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After the introduction in Section 1.1, we discuss general preliminaries (Section 1.2), preliminaries on linear algebra, matrix theory and Euclidean geometry (Section 1.3), and on graph theory (Section 1.4). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational linear inequalities, integral optimum solution, programming duality equation, given rational matrix, basis reduction method, dual integrality, linear diophantine problem, random linear programs, nonnegative integral combination, total unimodularity, symmetric travelling salesman problem, matching polytope, blocking polyhedra, pivot selection rule, vertex complexity, linear matroid, network matrices, integral polyhedron, polynomial solvability, simultaneous diophantine approximation, linear diophantine equations, lineality space, finite basis theorem, rational polyhedron, binary matroid Key Phrases - Capitalized Phrases (CAPs): (learn more)
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After the introduction in Section 1.1, we discuss general preliminaries (Section 1.2), preliminaries on linear algebra, matrix theory and Euclidean geometry (Section 1.3), and on graph theory (Section 1.4). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational linear inequalities, integral optimum solution, programming duality equation, given rational matrix, basis reduction method, dual integrality, linear diophantine problem, random linear programs, nonnegative integral combination, total unimodularity, symmetric travelling salesman problem, matching polytope, blocking polyhedra, pivot selection rule, vertex complexity, linear matroid, network matrices, integral polyhedron, polynomial solvability, simultaneous diophantine approximation, linear diophantine equations, lineality space, finite basis theorem, rational polyhedron, binary matroid Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fourier Motzkin, Application of Corollary, Apply Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
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100
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- A Source Book in Mathematics (Dover Books on Mathematics) by David Eugene Smith on 6 pages
- Discrete Mathematics by Wiley on 5 pages
- Linear Inequalities and Related Systems. (AM-38) (Annals of Mathematics Studies) by Harold William Kuhn on 5 pages
- Mathematical Programming: Structures and Algorithms by Jeremy F. Shapiro in Back Matter (1), Back Matter (2), and Back Matter (3)
- Operations Research (Business Statistics) by Wayne L. Winston in Back Matter (1), Back Matter (2), and Back Matter (3)
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- Linear Optimization and Extensions (Algorithms and Combinatorics) by Manfred Padberg on 4 pages
- Integer Programming and Combinatorial Optimization: 7th International IPCO Conference, Graz, Austria, June 9-11, 1999, Proceedings (Lecture Notes in Computer Science) by Gerard Cornuejols on 4 pages
- Integer Programming and Combinatorial Optimization: 11th International IPCO Conference, Berlin, Germany, June 8-10, 2005, Proceedings (Lecture Notes ... Computer Science and General Issues) by Michael Jünger on page 264, page 305, and Back Matter
- Lectures on Petri Nets I: Basic Models: Advances in Petri Nets (Lecture Notes in Computer Science) by Wolfgang Reisig on page 308, page 371, and page 586
- Structural Economics (Routledge Frontiers of Political Economy) by Thijs ten Raa on page 17, page 105, and page 128
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