Theory of Linear and Integer Programming by Alexander Schrijver (PDF)

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 index

User’s Reviews

Editorial Reviews: Review “…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 Inside Flap 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 From the Back Cover 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 About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐1. After deliberating over 4 weeks searching/reviewing for “the” right book that would complement my advance “Operations Research” studies I chose “Theory of Linear and Integer Programming” because it matched, paralleled and exceeded my studies for my MBA “Operations Research” which was completed in 20002. Part II is a very detail review of “matrices” and lattice applications which a review for me, because this was part of my education.3. Each of the nine chapters of part III is presented in a very detailed and precise method for understanding a very complex study of 1) Polyhedra, Linear Equations and Linear Programming4. After perusing Part IV “Integer Linear Programming” it appears that my expectations are extraordinarily surpassed because the author presents each of the nine topics with clarity and detail and I believe after a “very thorough studying” of each chapter carefully I will able to apply these complex methods of statistical analysis and forecasting on the data that I will be analyzing at work – Database/Forecasting modeling will be a crucial part of work tasks.

⭐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.

⭐It’s an excelent book, but in order to use it as a classroom book I will make two improvement1) Add an exercises section at the end of each chapter2) Deal more extensively with Mixed Integer Linear Programming problem, e. g. add the proof of the finiteness of the Gomory’s Cutting Plane Method.

⭐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.

⭐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.

⭐The book is a classic and the content is outstanding: the following comment only applies to the product itself, the physical book received.I have read on this online previously, and I have now a clear example of what seems a problem that may sometimes occur with the new ‘on demand printing approach’. Sure the price is decreased a bit but is very high here compared to the quality of the printing which looks like a photocopy of the original, including the white color paper and its quality (like ordinary paper used for photocopies …), the fuzzy color printed backcover, and some pages where letters fade, though everything of course is technically ‘readable’.Margins are quite high, so I do not understand the logic of not trying to achieve a good service level with again, what seems an ‘on demand printing’ approach problem.–> Can someone from Amazon and/or Wiley can confirm this ?–> Have you seen what is the product delivered ?Regards,MM

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