Linear Programming, Second Edition - Foundations and Extensions (International Series in Operations Research and Management Science, Volume 37) (International ... in Operations Research & Management Science)

Book Description

Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization.

The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.

Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied:

-The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods.

In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's webpage: . Also, check the book's webpage for new online instructional tools and exercises that have been added in the new edition.

Customer Reviews:

Professor Robert Freund's review.......2004-04-30

This is a much more detailed one as compared to the other two and was penned by MIT ORC Professor Robert Freund.

Summary. This book presents a thoroughly modern treatment of linear programming that achieves a healthy balance between theory, implementation, computation, and between the simplex method and interior-point methods. It's most novel feature is that it is written in a delightful and refreshing conversational style, that bespeaks the author's teaching style and relaxed wit. It is a pleasure to read: students will find the book to be friendly and engaging, while professors will find in the book a wealth of teaching material, nicely organized and packaged for classroom use. The book is also meant to be used in conjunction with a public-available website that contains software for various algorithms, additional exercises, and demos of algorithms.
The need for new linear programming textbooks. The world of linear programming has changed dramatically in the last ten years. For one thing, the incredible changes in computer technology have made it easy to solve truly huge LPs, and routine LP problems solve in fractions of a second even on a personal computer. As a result, the study of linear programming algorithms is of less interest to the casual student. (In a similar vein, we usually do not teach students how to efficiently compute square roots; we simply presume they can press the right buttons on their calculator.) On the other hand, because we can now solve truly gigantic linear programs, issues of computer implementation, numerical stability, and software architecture, etc., are as important for the serious optimizer as is, say, duality theory. Furthermore, the development and recognition of the importance of interior point methods has changed the landscape of linear programming significantly, so that linear programming is no longer synonymous with the simplex method, and a modern treatment of LP must also present an in-depth treatment of the most important interior point methods.

Vanderbei's book is thoroughly modern. Vanderbei's book is completely up-to-date. Aside from a nice treatment of the simplex method, it also contains a very up-to-date treatment of interior point methods, including the homogeneous self-dual formulation and algorithm (which might soon become the dominant algorithm in practice and theory). It contains extensive material on issues of implementation of both the simplex algorithm and interior point algorithms. A politician might call it a book for the 21st century.

Vanderbei's book has many novel features. This book is quite different from most other textbooks on LP in a number of important ways. For starters, the standard form of a linear program in the book is the symmetric form of the problem (max c^T x | Ax <= b, x >= 0), as opposed to the usual form (min c^T x | Ax=b, x >= 0). This difference allows for an easier treatment of duality, and allows one to see the geometry of linear programming more easily as well. The symmetric form also makes it easier to set up the homogeneous self-dual interior point algorithm. However, this form has the drawback that discussions of bases, basic feasible solutions, and some of the mechanics of the simplex method are all a bit more awkward. (The book uses the language of dictionaries to describe the essential information in a simplex method iteration.) The book has more of a focus on engineering applications than does the more typcial LP textbook (which tend to rely on business problems). For example, there is a nice chapter on optimization of engineering structures such as trusses. The book gives a very broad treatment of interior point methods, including several topics that are not usually found in textbooks such as the homogeneous self-dual formulation and algorithm, quadratic programming via interior point methods, and general convex optimization via interior point methods.

These novel features are good in that the author has clearly tried to be innovative and to build an LP text from the ground up, without regard for past texts.

Some Nice Features. There are some particularly nice features in the book. The book contains a much-simplified variant of the Klee-Minty polytope that allows for a more straightforward proof that the simplex method can visit exponentially many extreme points. In addition to proving strong duality, the book also presents Tucker's strict complementarity theorem, which has become important in the new view of sensitivity analysis, optimal partitions, and interior point methods. The book also contains a nice treatment of the steepest edge pivot rule, which has recently emerged as an important component in speeding up the performance of the simplex algorithm. In the treatment of interior point methods, the author spends very little time on polynomial time bounds and guarantees (as a theorist, I like to see this material), instead adding value by discussing important computational and implemention issues, including ordering heuristics, strategies for solving the KKT system by Newton's method, etc. The book sometimes has an engineer's feel for the proofs, which is good for students but is a bit frustrating to hard-core math types such as myself. There are many instances where the proof is just a proof via an example. This is consistent with the conversational and informal style of the text, and this informality spills over into the mathematics on occasion.

This book has style. As mentioned earlier, the book has a wonderfully appealing conversational style. While the author does not purposely go out of his way to be cute and corny, he succeeds in leaving the reader grinning with his humor. There are some passages that are downright funny, but the style succeeds mostly by default. One section on the issue of modeling the anchoring of truss design problems is called Anchors Away, the subsection on updating factorizations to reduce fill-in is aptly called Shrinking the Bump. And there is the hint of a racy discussion of an application of Konig's Theorem involving boys and girls that the curious reader might enjoy.

Overall, I greatly enjoyed reviewing this book, and I highly recommend the book as a textbook for an advanced undergraduate or master's level course in linear programming, particularly for courses in an engineering environment. In addition, the book also is a good reference book for interior point methods as well as for implementation and computational aspects of linear programming. This is an excellent new book.

Excellent book.......2002-07-18

Very clearly written. Unlike most math books, the notation is easy to understand for engineers and programmers. I found the free online version first, and then decided to buy the hard copy.

Profesor.......2001-04-11

That book is excelent from class and practice. Very important in undergraduate and postgraduate. Thanks you.

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Review of Dantzig's book

Linear Programming and Extensions
George Dantzig
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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Linear Programming 2: Theory and Extensions
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Linear Programming: Methods and Applications: Fifth Edition
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An Illustrated Guide to Linear Programming

ASIN: 0691059136

Book Description

In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered.

George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems.

Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.

Customer Reviews:

Review of Dantzig's book.......2007-05-08

This softbound newly reprinted edition is clear and light; considering the original version I knew back in 1970's was a thick, heavy hardbound.

The book is a compilation of several authors on linear programming, it includes a table explaining the genesis of linear programming and the programming code for computer calculation.

It is a rich and indispensable book for optimization problems.

Linear Optimization and Extensions (Algorithms and Combinatorics)

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Computational and Mathematical Excellence
A good reference for Linear Programming Theory

Linear Optimization and Extensions (Algorithms and Combinatorics)
Manfred Padberg
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Network Flows: Theory, Algorithms, and Applications
Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6)

ASIN: 3540658335

Book Description

This book offers a comprehensive treatment of linear programming as well as of the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. An introduction surveying fifty years of linear optimization is given. The book can serve both as a graduate textbook for linear programming and as a text for advanced topics classes or seminars. Exercises as well as several case studies are included. The book is based on the author's long term experience in teaching and research. For his research work he has received, among other honors, the 1983 Lanchester Prize of the Operations Research Society of America, the 1985 Dantzig Prize of the Mathematical Programming Society and the Society for Industrial Applied Mathematics and a 1989 Alexander-von-Humboldt Senior U.S. Scientist Research Award.

Customer Reviews:

Computational and Mathematical Excellence.......2002-05-26

For nearly 30 years, Padberg has been a leader in computational integer programming and in combinatorial optimization theory.

In practice, Padberg has helped to design and implement "branch-and-cut" methods for finding exact optimal solutions to large traveling salesman problems, and this approach is a method of choice for finding approximately optimal solutions to tough industrial problems. The book provides the mathematical and computational background for understanding branch-and-cut; the established mathematical texts by Nemhauser and Wolsey and by Schrijver are less detailed and more condensed, and omit numerical issues. The treatment of modern simplex algorithms for linear programming---updating LU factorizations and using column- and constraint-generation and -purging---is excellent, and a large bibliography contains recent references. Besides industrial and Berlin-airlift scheduling problems, the book contains TSP examples of circuit-board wiring, U.S. state capitals, and Odysseus!

Three more highlights: The double description algorithm receives a complete description, and this is useful for combinatorial geometers. The discussion of integer-arithmetic and complexity theory is very readable, and these technical topics are slighted by interior-point books (besides Wright's quickie), despite their importance in integer programming and combinatorial optimization. The discussion of interior-point algorithms emphasizes projective geometry, a beautiful theory that has inspired so much of optimization theory---besides Karmarkar's interior-point algorithm, Dantzig's simplex algorithm, Fenchel duality, Davidon's conic algorithm for nonlinear optimization, etc.).

The book is not a comprehensive survey of linear programming,
and lacks a treatment of Nesterov's theory of self-concordant barrier-functions. Also, no treatment is given of pivoting algorithms besides Dantzig's (e.g., Terlaky's criss-cross method, Todd's oriented matroid algorithm).

A good reference for Linear Programming Theory.......2000-06-01

This book is certainly a very good reference for theoretical topics of linear programming. It covers the Simplex method and the Ellipsoid algorithms. It also covers the geometry of linear programming (polyhedra and polytopes, etc). It certainly covers more topics than most other linear programming texts. As expected, a book writen for theoretical topics is certainly not easy to read, especially for people with no training in doing rigorous mathematical proofs. Also, not many examples or illustrations are given in this book, and this might be a problem for some readers.

A buyer-seller game model for selection and negotiation of purchasing bids: Extensions and new models [An article from: European Journal of Operational Research]

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A buyer-seller game model for selection and negotiation of purchasing bids: Extensions and new models [An article from: European Journal of Operational Research]
J. Zhu
Manufacturer: Elsevier
ProductGroup: Book
Binding: Digital

Elsevier | By Publisher | e-Docs | Formats | Books
ASIN: B000RR0VFU

Book Description

This digital document is a journal article from European Journal of Operational Research, published by Elsevier in 2004. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
A number of efficiency-based vendor selection and negotiation models have been developed to deal with multiple attributes including price, quality and delivery performance. The efficiency is defined as the ratio of weighted outputs to weighted inputs. By minimizing the efficiency, Talluri [Eur. J. Operat. Res. 143(1) (2002) 171] proposes a buyer-seller game model that evaluates the efficiency of alternative bids with respect to the ideal target set by the buyer. The current paper shows that this buyer-seller game model is closely related to data envelopment analysis (DEA) and can be simplified. The current paper also shows that setting the (ideal) target actually incorporates implicit tradeoff information on the multiple attributes into efficiency evaluation. We develop a new buyer-seller game model where the efficiency is maximized with respect to multiple targets set by the buyer. The new model allows the buyer to evaluate and select the vendors in the context of best-practice. By both minimizing and maximizing efficiency, the buyer can obtain an efficiency range within which the true efficiency lies given the implicit tradeoff information characterized by the targets. The current study establishes the linkage between buyer-seller game models and DEA. Such a linkage can provide the buyer with correct evaluation methods based upon existing DEA models regarding the nature of bidding.

DLP and Extensions: An Optimization Model and Decision Support System

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DLP and Extensions: An Optimization Model and Decision Support System
John L. Nazareth
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540411143

Book Description

DLP denotes a dynamic-linear modeling and optimization approach to computational decision support for resource planning problems that arise, typically, within the natural resource sciences and the disciplines of operations research and operational engineering. It integrates techniques of dynamic programming (DP) and linear programming (LP) and can be realized in an immediate, practical and usable way. Simultaneously DLP connotes a broad and very general modeling/ algorithmic concept that has numerous areas of application and possibilities for extension. Two motivating examples provide a linking thread through the main chapters, and an appendix provides a demonstration program, executable on a PC, for hands-on experience with the DLP approach.

Extensions and Relaxations (Mathematics and Its Applications)

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Extensions and Relaxations (Mathematics and Its Applications)
A.G. Chentsov , and S.I. Morina
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402005792

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In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of a system of constraints. This construction is realized in a special class of generalized elements defined as finitely additive measures. A version of the method of programmed iterations is constructed. This version realizes multi-valued control quasistrategies, which guarantees the solution of the control problem that consists in guidance to a given set under observation of phase constraints.

Audience: The book will be of interest to researchers, and graduate students in the field of optimal control, mathematical systems theory, measure and integration, functional analysis, and general topology.

Extensions of Logic Programming: 5th International Workshop, ELP '96, Leipzig, Germany, March 28 - 30, 1996. Proceedings. (Lecture Notes in Computer Science)

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Extensions of Logic Programming: 5th International Workshop, ELP '96, Leipzig, Germany, March 28 - 30, 1996. Proceedings. (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540609830

Book Description

This book constitutes the refereed proceedings of the 5th International Workshop on Extensions of Logic Programming, ELP '96, held in Leipzig, Germany in March 1996.The 18 full papers included were carefully selected by the program committee and are presented together with three invited papers. Among the topics addressed in this book are categorical logic programming, correctness of logic programs, functional-logic languages, implementation issues, linear logic programming, nonmonotonic reasoning, and proof search.

An introduction to nearly optimal programming an extension of sensitivity analysis in linear programming.: An article from: Education

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An introduction to nearly optimal programming an extension of sensitivity analysis in linear programming.: An article from: Education
John T. Quinn , and Kristin T. Kennedy
Manufacturer: Project Innovation (Alabama)
ProductGroup: Book
Binding: Digital

Book Description

This digital document is an article from Education, published by Project Innovation (Alabama) on December 22, 1993. The length of the article is 5437 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: An introduction to nearly optimal programming an extension of sensitivity analysis in linear programming.
Author: John T. Quinn
Publication: Education (Refereed)
Date: December 22, 1993
Publisher: Project Innovation (Alabama)
Volume: v114 Issue: n2 Page: p209(12)

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Linear Programming 2: Theory and Extensions

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interesting book

Linear Programming 2: Theory and Extensions
George B. Dantzig , and Mukund N. Thapa
Manufacturer: Springer
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Binding: Hardcover

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Linear Programming: 1: Introduction (Springer Series in Operations Research and Financial Engineering)
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ASIN: 0387986138

Book Description

Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method, interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering, and applied mathematics will find this volume of particular interest.

Customer Reviews:

interesting book.......2006-02-24

There is an example of piecewise linear convex problem which I was looking for.

Linear Programming and Extensions (Mcgraw Hill Series in Industrial Engineering and Management Science)

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Linear Programming and Extensions (Mcgraw Hill Series in Industrial Engineering and Management Science)
Nesa L'Abbe Wu
Manufacturer: Mcgraw-Hill College
ProductGroup: Book
Binding: Hardcover

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ASIN: 0070721173

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