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.

Customer Reviews (3)

Professor Robert Freund's review
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
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
That book is excelent from class and practice.Very important in undergraduate and postgraduate.Thanks you. ... Read more

Book Description

"Linear and Nonlinear Programming" is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first and second editions.Now the third edition has been completely updated with recent Optimization Methods.Yinyu Ye has written chapters and chapter material on a number of these areas including Interior Point Methods.

Customer Reviews (5)

Good book , but consider a used copy!
Luenberger's optimization book is very good and well worth having.However, it should be noted that the "new" 2004 edition published by Springer-Verlag is nothing more than an exact reprint of the 1984 2nd edition that was formerly published by Addison-Wesley.Accordingly, a good used copy may be more worthwhile than an overpriced "new" one.

This is the fourth such case I have come across wherein a publisher chooses to engage in such misleading marketing practices.The other three are "Engineering Optimization - Methods and Applications" by Reklaitis (1983), "Hydraulic Control Systems" by Merrit (1967), and "Dynamic Systems" also by Luenberger (1979).All three are now being sold as new publications by Wiley (according to Amazon).I suspect there are many other examples as well.

The book is a Xerox
Looking from outside, the book seems very good. However, when you open the cover you are shocked by the press quality. It seems like the book just came from an illegal copy shop. Sometimes you can not read small indices in formulas. For a book having this context, a better press quality should be used. I could make a better copy with a copy machine.The paper quality is around average.

A book on mathematics that also an engineer can read
I have profitably used the book to apply constrained minimization procedures in the field of computational contact mechanics. I think it is not a secret that quite often books on mathematics are written frommatematicians for matematicians. Hence it is quite hard for engineers bothto read and to extract valuable information from them. With this respectthis book is a shining star. It presents the topics in a very precise butclear and understandable way. Moreover the notation also is the bestcompromise between coinciseness and clarity. Matematicians, please, look atthis book and follow such style; we engineer desperately need tocommunicate with you.

A necessary book for all who want to read and learn!
I have the 1977 edition from my father's MIT days. I am a Mathematician and I can verify that the book written in 1977 is of the same style that good books have today! A book is not made obsolete because some new"elegant" terms arise. Ok Luenberger did not know about InteriorPoint Algorithms and to tell you the truth why should he? I do not knowother editions but in the first edition in chapter 7 "Basic DescentMethods" everyone who is able to read clearly and unbiased the secondparagraph will agree with me that Interion Point Algorithms IS NOTHING NEWin the theory of MATHEMATICS!!! What you need to know ,the magic, is in thechapters 7-11. From there you can read everything else you like and get intouch with what is about to come in the next 25 years(See Ye :"Interion Point Algorithms"). But remember you are already instars before reading the new books...

Good introduction
Nice introduction to linear programming, but new standard definitions have already arrived, making many "good books" obsolete. The book sometimes isn't very clear and should be more explicit and should give more examples. ... Read more

Book Description

Customer Reviews (5)

An Illustrated Guide to Linear Programming
The book is very good for introducction to the applications of Linear Programming. It will be useful for first time students of Operations Research.The explaination is very simple and innovative. The later part of the book introduces matrix algebra which is the gist of Linear Programming at the advanced stage.

An effective introduction to Linear Programming
For someone with an interest in learning LP but not the best mathematical foundation for learning it, this book worked for me. I think the author is an experienced teacher of people with math skills such as mine and knew how present the material and explain it in familiar terms.
The book does not have all the material I need but did get me going in a confident manner so I could handle the other books I bought before I bought this one.

Great intro to Linear Programming
This book is a great non-technical introduction to a very technical subject: linear programming. If you are interested in linear programming but you don't want to all of the mathematical details, then buy this book. Hey, you can't beat the price.

By the way, how can anyone expect a book like this to tell someone how to apply linear programming. Doing that requires a lot more technical training and there are other more detailed and more expensive books that explain how to apply linear programming. This book is a great introduction a complicated subject. You will enjoy this book if your expectations are reasonable.

Good, but a reprint from 1970
This book presents a good conceptual overview of linear programming, geared for the non-mathmatical person. However, it is a reprint of a 1970 title, so there isn't much on the use of computers to solve this type of problem.

An Illustrated Guide to Linear Programming
This book is an excellent treatment of linear programming for non-technical people.It describes a number of basic business-world applications that can be readily solved using standard linear programmingmethods.I recommend it highly because it presents the complex principlesof this important methodology in an easy-to-read manner. ... Read more

Book Description
Linear Programming and Network Flows, now in its third edition, addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequility constraints. This book:
* Provides methods for modeling complex problems via effective algorithms on modern computers.
* Presents the general theory and characteristics of optimization problems, along with effective solution algorithms.
* Explores linear programming (LP) and network flows, employing polynomial-time algorithms and various specializations of the simplex method. ... Read more

Customer Reviews (11)

Very Theoretical but good fundamental and advanced techniques
The techniques described are very theoretical but are friendly to be used in Computer programs. Has a great deal of depth.

This book is only useful if you already know about linear programming.
I am using this book for a linear programming course.The most flagrant problem with this book is that it is filled with typos, making reading through proofs and examples very frustrating because you're never sure what is supposed to be written.The book is also not very good at explaining concepts and leaves many steps out in the development of new ideas.If you can avoid it, do not use this book to learn linear programming.

It Could be better
In my point of view this book has 2 related problems:

Problem 1. It tries to pack much information in a small space.

Problem 2. I dont like the author's style of asking why? and how? to the reader in the midst of the text. Maybe this is to keep the book small but it forces you to stop reading and think about the question.


However, I think this book is a good reference. But, certainly the authors could have made it better. Let's wait for the next edition.

Strong Graduate Treatment in Linear Programming
I used this text while taking a graduate linear programming (LP)course on LP and network flows.I really liked the treatment.The typesetting was clear ,consistent and easily followed (not as good as Nash and Sofer's).The book also includes lots of nice side discussion on how or why the theory is the way it is.Plenty of references are offered for further study.Proofs were not rigorous.The highly mathematical reader may be disappointed by the "show proof" style used instead of a rigorous theorem-proof style.In fact, I seem to recall a time or two where the theorem came after the usage.For me, I didn't mind that, but a pure math guy would likely grind his teeth.

The network material was acceptable.I personally thought the text problems were not of the best quality.I would suggest a teacher supplement their own favorites outside of the book.

One caution is that the book is somewhat aged.I noticed a text like Nash and Sofer seems to have newer updates on the theory.

Overall, a great read for getting into the nitty gritty details of LP.

Excellent but DENSE!!!!
I am currently working toward a Ph.D. in Management Science and used this book for a LP course.If you can get past the matrix algebra (which isn't too terribly difficult) you will find that this book contains more practical LP information than any other resource available.However, those looking for a "how to" book on linear programming might want to try a more elementary text first.This book is geared toward those interested in the more advanced computational aspects of LP (e.g., revised simplex method, LU decomposition, product form of the inverse, bounded variables, etc.).The chapter on sensitivity analysis is particularly well written and thorough.But beware, this book packs more info per page than I have ever seen!!! ... Read more

Book Description

Customer Reviews (2)

A solid companion
If you are really interested in Linear Programming this book makes a great resource. It also makes a good companion book if you are studying Operations Research, as the LP component is comprehensive. The book gives a good explanation of the revised simplex method and duality problems. Also,sensitivity analysis is explained and demonstrated in a very straightforward and easy to understand manner.

Linear Programming: Methods and Applications: Fifth Edition
This book is excellent for everyone who is studying Linear Programming. What is especially useful is the large number of references that are included at the end of each chapter. The second thing is the inclusion of introductory material in chapters 1 to 4 for the first time student. The third thing that is good is the inclusion of many applications, making the book very useful for the experienced student of Operations Reserch. The fourth is the abundance of exercises at the end of each chapter. I strongly recommend this book for students, especially those who are from disciplines outside Mathematics, who will use computational techniques of Linear Programming. ... Read more

Book Description
Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations.
The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications.
The disk that comes with the book contains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers.

* More review material on linear algebra
* Elementary linear programming covered more efficiently
* Presentation improved, especially for the duality theorem, transportation problems, the assignment problem, and the maximal flow problem
* New figures and exercises
* Computer applications updated
* Added disk with the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University
* New guide to inexpensive linear programming software for personal computers ... Read more

Product Description
This book provides a unified, insightful, and modern treatment of linear optimization, that is, linear programming, network flow problems, and discrete optimization. It includes classical topics as well as the state of the art, in both theory and practice. ... Read more

Customer Reviews (10)

Par Excellence!
This book is THE best LP book I have come across. The topics are very clear and presented in the best possible manner. Introduces you to several basic and advanced LP topics, theorems and algorithms. The exercises at the end of each chapter test the students' understanding in an appropriate manner. A good number of examples are given to explain the theory in a better way. I would definitely recommend this book to a student interested in learning about optimization procedures and/or algorithm development.

Surely helps if you have taken a linear algebra course before. Some students who haven't had a linear algebra course find the math nomenclature formidable in the beginning.

Quite good
This book is impressive for theory, every thing you ever wanted to know or how to avoid some other is here. I teach to industrial engineering students, so i have to use other books for the application, but for the theory, everything is covered here, even more, in the book are several simple rules to avoid tipical problems of the simplex method or transportation problems, or integer forms. You can't call yourself a pro if you haven't read this book.

Nice intuition and good coverage
The best part of this book is the first half, where the foundations of linear programming are presented in a clear yet relatively rigorous fashion, accompanied by numerous intuitive geometrical explanations of the abstract general concepts. This approach, supplementing mathematics with graphical insights, works extremely well for this topic.

The quality goes down somewhat, perhaps neccessarily, in the latter half of the book as topics are presented less carefully, and in a somewhat rushed manner in order to cover all of the material the authors decided to include. Given that the fundamentals are covered so well, perhaps this is a fair trade.

The only real negative I can think of is that it's a small crime for professors to create their own publishing companies (Athena only publishes works by a small group of MIT professors) and then still charge outrageous amounts for the books. This would be completely unacceptable were it not for the fact that, unlike most self-published work, this book's production quality is on par with that of the large publishers.

Too Verbose
Most part can be expressed in a more terse way and with math language. However, the book revolve around using very lengthy sentence to explain, which is not so helpful and clear as expressed with math. It can be condensed to half thickness.

A+++
Exactly as described, fast delivery. I will always try to choose amazon from now on. ... Read more

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 (2)

good to have but not to learn from
I disagree with the other reviewer.This is a textbook on linear programming and its extension written by George Dantzig the inventor of the simplex method.Even though the simplex method is still popular and useful there are other interesting algorithms that were dsicovered in the 1980s and 1990s that have theoretical and in some cases practical value.

In 1974 I was a graduate student in Operations Research ae Stanford and I took the three quarter mathematical programming course sequence.The first two quarters were taught by George Dantzig out of this book.George was a delightful person to talk to and probably a good thesis advisor and his stories about his graduate school days and the early years at RAND are delightful.However his lectures were disorganized and vague.I found it impossible to learn much from them and the book was not much help either as it too was vague, disjointed and not well organized.Better understanding of the basics of linear programming can be gotten from the fine general books on operations research such as the book by Hillier and Lieberman and the one by Wagner.

I do not know what is the best modern book on linear programming is.It should have good coverage of the simplex method and a lot of applications. Leontiff systems and other special structured programming problems that lead to modifications of the simplex method are covered in this book and should also be in the "ideal" linear progamming book.Integer programming and other special cases of problems with linear constraints should also be included along with alternative algorithms to the simplex method.

This book is more valuable for historic purposes, as it was Dantzig's first book and the first account of the simplex method by its inventor.

Review of Dantzig's book
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.

... Read more

Book Description

Customer Reviews (3)

A classical book.
This book is a classical. It's important you'll buy for your library.

Good if you care more about the economics than the math...
I have to agree with the other reviewer, this is a fantastic book. It explains very clearly how powerful a tool linear programming can be in economics. However, this book really ties its hands by only talking aboutmatrices or any of the mathematical reasons why linear programming works asit does in an appendix. If you're a mathematician that wants to learn aboutlinear programming, this is definitely not the book. But if you're aneconomist, or just someone interested in economics, that wants to learnabout linear programming, then this book is definitely for you. It is veryrich with economic ideas and covers a lot of interesting topics such asgrowth theory and welfare economics.

VER GOOD
I LÝKE THÝS BOK ÝT'S FANTASTÝ ... Read more

Customer Reviews (7)

An OR professor's review
The book presents many aspects of linear programming, particularly basic concepts, in a much simpler and interesting way than earlier books on this area.If focuses on what I consider the relevant aspects of LP and avoids sections describing endless calculations. Besides basic and some advanced concepts, there is an entire section devoted to applications which is interesting for engineering courses.

Linear Programming as Mathematics
I've been teaching a linear programming course at the advanced undergraduate level out of this book for the last 12 years.I'm still happy with Chvatal's book and haven't found anything better.

Prerequisites for this book include some background in linear algebra (the typical sophomore level introduction to linear algebra is enough), and some experience with proof based mathematics.Because the subject does not involve the difficult concepts of analysis, it (much like number theory) makes a good subject for students to study as they are developing proof writing skills.

The first 10 chapters of the book present the simplex method, the revised simplex method, duality theory, and sensitivity analysis.
This material can easily be covered in 10 weeks.The remaining chapters of the book are largely independent, mostly focused on various applications of linear programming and specialization of the simplex method to network flow problems.

Chvatal presents the simplex method and many of its applications from a mathematical point of view.He states and proves theorems,but also provides plenty of motivation.Students who make an effort do develop more mathematical maturity from working through this book.

Chvatal also presents the material from a computational and algorithmic point of view.One of the major points of the book is that the author prefers to use algorithmic proofs.For example, the proof that every standard form LP is either infeasibile, unbounded, or has an optimal BFS is built on the simplex method-Since the algorithm terminates in one of these three states, and can't go into an infinite loop, these are the only possibilities.

Another particular strength of the book is in the presentation of duality theory.The explanation is simply very clear and intuitive.

The one glaring weakness of the book is that it doesn't contain any discussion of interior point methods for linear programming.Since the book was published in the mid 1980's, this is not surprising.In my course, I supplement Chvatal's book with my own lecture notes on interior point methods.

garbage
i don't understand why everyone is giving this book such great reviews.as a linear programming student, i find this book extremely difficult to understand, very poorly orgranized, extremely lacking in practical examples to demonstrate the concepts that the author is attempting to describe, and basically a piece of garbage.it was obviously written by a mathematician, not someone capable of teaching.i would not recommend it to anyone.

It's a Keeper
I cut my teeth on this text in George Nemhauser's class. The book is clear and concise and does an excellent job explaining this topic to beginners. I've not come across a better introductory text yet. I still have this book in my reference library.

If you want an introduction to LP, this is the text for you.

An excelent book on LP
The book offers an objective treatment of linear programming, in small self contained chapters. I consider this title the best introdutory text on LP, just because it is extremely well written. The major drawback of this book is the small and easy number of exercises proposed at the end of the chapters. The text is not an updated book on the subject, but I really recomend it. ... Read more

Book Description

Book Description
The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes". ... Read more

Customer Reviews (1)

Amazing linear programming book
This is one of the greatest linear programming books I've ever read.

It sets out to teach linear and it only does that. It does not go into any neigbour topics and confuse the reader.
It is also picky about the proofs it provides, only the necessary ones.

Finally, I also liked the way they introduced the simplex tableus. They completely avoided the more usual tableau look. Instead they only show the equations which form the tableau. This makes simplex much more understandable.

All in all, great book for new grad students in industrial engineering, computer science, etc... ... Read more

Book Description
The effectiveness of the algorithms of linear programming in solving problems is largely dependent upon the particular applications from which these problems arise. A first course in linear programming should not only allow one to solve many different types of problems in many different contexts but should provide deeper insights into the fields in which linear programming finds its utility. To this end, the emphasis throughtout Linear Programming and Its Applications is on the acquisition of linear programming skills via the algorithmic solution of small-scale problems both in the general sense and in the specific applications where these problems naturally occur. The first part of the book deals with methods to solve general linear programming problems and discusses the theory of duality which connects these problems. The second part of the book deals with linear programming in different applications including the fields of game theory and graph theory as well as the more traditional transportation and assignment problems. The book is versatile; in as much as Linear Programming and Its Applications is intended to be used as a first course in linear programming, it is suitable for students in such varying fields as mathematics, computer science, engineering, actuarial science, and economics. ... Read more

Customer Reviews (1)

highly erudite
I took the class for which this book was used as a sophomore, and found it to be very accessible.In retrospect, I would have liked to have studied some linear algebra before having taken this course, but still, I foundthis to be a very interesting course as a stand-alone. ... Read more

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. ... Read more

Customer Reviews (1)

interesting book
There is an example of piecewise linear convex problem which Iwas looking for. ... Read more

Book Description
This textbook provides a self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interior-point methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and senior-level undergraduate students, first-year graduate students, and researchers unfamiliar with linear programming. ... Read more

Book Description
A practical, accessible guide to optimization problems with discrete or integer variables

Integer Programming stands out from other textbooks by explaining in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems, such as airline timetables, production line schedules, or electricity production on a regional or national scale.

Incorporating recent developments that have made it possible to solve difficult optimization problems with greater accuracy, author Laurence A. Wolsey presents a number of state-of-the-art topics not covered in any other textbook. These include improved modeling, cutting plane theory and algorithms, heuristic methods, and branch-and-cut and integer programming decomposition algorithms. This self-contained text:
* Distinguishes between good and bad formulations in integer programming problems
* Applies lessons learned from easy integer programs to more difficult problems
* Demonstrates with applications theoretical and practical aspects of problem solving
* Includes useful notes and end-of-chapter exercises
* Offers tremendous flexibility for tailoring material to different needs

Integer Programming is an ideal text for courses in integer/mathematical programming-whether in operations research, mathematics, engineering, or computer science departments. It is also a valuable reference for industrial users of integer programming and researchers who would like to keep up with advances in the field. ... Read more

Customer Reviews (4)

Very good!
It has all the major subjects in IP and uses a mathematical approach very clear.

Integer Programming
It's not good for the beginners who never have basic knowledge about linear, nonlinear, and integer programming. Too difficult to understand because it contains only theories.

One of the most interesting books I've used
This book features great contents. Integer programming is one of the most interesting subjects and this book captures the beauty of it through the use of nice explanations and a neat and organised notation. The author carefully describes the algorithms used to solve some of the classic integer programming problems. The theorems are generally followed by proofs and the contents are presented in a very comprehensive order.

A Complete Referance
I really like reading this book. It is upto date in terms of algorithms and theory. You can find nearly every basic topic about integer optimization in the book. I consider it as a complete referance in integer optimization. The sequence of the topics, chapters, also make it easier tounderstand the contents. The book gives both the theory and solutionstrategies. I recommend the book for people who work or study in thefollowing areas:industrial engineering, operations research and operationsmanagement. ... Read more

Book 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 ... Read more

Customer Reviews (4)

Good book
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.

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

Advanced LP and IP book
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.

An Eyclopedic reference for linear and integer prog.
A great reference text book, with some great historicalnotes 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 andInteger Programming. ... Read more

Book Description
This book provides a comprehensive introduction to linear programming which encompasses all the major topics students will encounter in courses on the subject. The authors aim to teach both the underlying mathematical foundations and how these ideas are implemented in practice. The book illustrates all the concepts with both worked examples and plenty of exercises. In addition, Windows software is provided with the book so that students can try out numerical methods using the examples and exercises and hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time.
Authors'note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States. The new version of Formula One, when ready, will be posted on WWW. ... Read more

Book Description
"Combines the theoretical and practical aspects of linear and integer programming. Provides practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming, as well as real-world solutions to the transportation and transshipment problem, project scheduling, and decentralization." ... Read more

Book Description

Peter Kall and János Mayer are distinguished scholars and professors of Operations Research and their research interest is particularly devoted to the area of stochastic optimization. Stochastic Linear Programming: Models, Theory, and Computation is a definitive presentation and discussion of the theoretical properties of the models, the conceptual algorithmic approaches, and the computational issues relating to the implementation of these methods to solve problems that are stochastic in nature. The application area of stochastic programming includes portfolio analysis, financial optimization, energy problems, random yields in manufacturing, risk analysis, etc. In this book, models in financial optimization and risk analysis are discussed as examples, including solution methods and their implementation.