Product 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

Customer Reviews (1)

Weak on theory and
This book was used for a graduate course in LP.For that purpose it was very weak.It takes a practical view of LP and relates it to Matlab, just as the title suggests.I found its content more applicable to undergrads than grads.

On the positive side, the book includes a large set of Matlab routines for manipulating LP tableaus.The support routines are great for solving problems quickly.

I would not recommend this for graduate work.I like Bazaraa's treatment of this subject much better.This book might be OK for professional work if you need a practical intro. ... Read more

Product 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

Customer Reviews (1)

Bad condition
I never buy used textbooks and decided to buy one this time. The seller described the book as very good. When I received the book, the first chapter was falling out. There is highlighting and writing all over the book. The book is well used and old. I personally would not call this very good condition. ... Read more

Product 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

Customer Reviews (1)

Clear and concise
I haven't seen this book for over a decade, but I do remember it helping me solve a problem way back when I was still an undergraduate. The summer after my junior year of university I was working at a steel foundry and they asked me to write a program for them that would solve their steel mixture problem in an optimal way. Their old software did this, but ran on a 286 PC and was slow and could not be ported to anything newer. I figured "no problem" and thought for sure that all this would involve was computing a few derivatives. A week into the problem, I found I was wrong and was quickly introduced to the world of linear programming.

I freaked out a little, and wasn't sure how to go about solving my problem. Strang mentions LP in his classic linear algebra book, but his exposition is very terse and entirely theoretical... entirely useless to a newbie needing to solve a real problem.

Then I found Dantzig's book. I was saved. I understood exactly what he was talking about and how everything worked. I was able to write a simplex based optimal solver for the steel formulation problem, which is simply the classic mixtures problem. The book also helped me with the optimal update solution for cases in which the chemistry of the first try was out of spec due to errors in estimates of the chemical compositions of the materials used in the initial charge.

My code was probably pure spaghetti, written in VBA no less using MS Access 97, but it worked very well. The old code on the 286 took around 30 seconds or longer to solve the problem, and my code running in VBA on a Pentium II solved the problem instantaneously. I owe my salvaged nerves to this book. ... Read more

Product 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

Product Description
Unlike other fractional programming related titles, this bookoffers a "direct" approach to LFP and to duality in LFP, which is newin many aspects. First, the original LFP problem is considered as itis, without reducing it to an LP problem. Moreover, LFP is consideredto be a generalization of LP and so most of the results are formulatedin such a way that appropriate results of LP may be obtained as aspecial case of LFP. On the other hand, this approach makes itpossible to compare dual variables in LP and LFP and to describe therelationship between them. In this respect, important (and new)application possibilities of duality appear in different parts of thebook. The book provides readers with the basic knowledge necessary to buildLFP models, to solve LFP problems and to utilize the optimal solutionobtained. Moreover, the book contains detailed information on WinGULF,a software package developed by the author especially forlinear-fractional programming. The package is designed to solve LFPproblems with continuous as well as integer variables. The special"Student Edition" version of the package is free of charge and may bedownloaded from the author's web page. Audience: The book is suitable for researchers in mathematicalprogramming, scientists and professionals who work in optimization,and also students who wish to expand their knowledge beyond a standardcourse of linear programming. ... Read more

Product Description

Product Description
Praise for the Second Edition:

"This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."
—Mathematical Reviews of the American Mathematical Society

An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems.

This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel®, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel® is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications.

Additional features of the Third Edition include:

• A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models

• Revised proofs and a discussion on the relevance and solution of the dual problem

• A section on developing an example in Data Envelopment Analysis

• An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games

Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science. ... Read more

Customer Reviews (2)

A good introductory book
The first part of this book is a good introduction to linear programming and the simplex method. Easy reading, tries to give insight, and with lots of examples. My personal favorite when it comes to refreshing my intuition on duality and how simplex works.
Regarding the game theory material, it seems to be a little crowded. Don't expect any in-depth coverage there, but as a brief overview it might be appropriate.

Not well-organized
After spending much of the summer reading and trying to learn linear programming on my own using this book, I feel that I'm qualified write this review.

This book suffers from persistent disorganization which I suspect is due to pressure put on the author to reduce the number of pages in the book as much as possible.Consequently, formatting shortcuts are taken wherever possible.Some of these shortcuts do not seriously inhibit learning this material.

But when one wishes to complete a problem which requires that you refer to a problem 2 chapters before; which requires that you refer to a problem one chapter before, and so on.And when a specific example refers to a problem two sections before, which refers to a table two sections before that, which...well you get the point.The reader is then required to focus more on what page what table is then on the material.

The other major difficulties with this book arise from the authors lack of good punctuation and his lack of emphasis (through formatting on the page itself) of important points, often contained deep within examples.Most of the topics of the first 5 chapters are taught in the form of an example.And so a single sentence within a half-page paragraph of information that is critical to understanding the problem at hand ought to be emphasized some how.Some people prefer bold such things, others prefer to center.Dr Thie prefers to have you reread a huge paragraph of information on a page you can't remember to find out if such and such number was required to be positive or negative.

That's my take.You get the picture.Don't buy this book unless your prof makes you. ... Read more

Product Description
This book makes Linear Programming easily accessible to any reader, regardless of his or her mathematical background.The emphasis on logic and modeling of applications enables those will little mathematical background to learn to use Linear Programming in their respective fields (business, economics, operations research, etc.).This book is useful for anyone interested in learning real-world applications of mathematics or for computer scientists who want to test their programming skills. ... Read more

Customer Reviews (1)

Great book for learning on your own
I was actually a student in Professor Byrne's class at Penn State University when he and Professor Vaserstein were working on the book. The bulk of the course material and layout of that course eventually became the core of this book. This is good because the course was excellent. With no experience in LP (linear programming) you easily move through this book from cover to cover. Both graphical and SIMPLEX methods are thoroughly discussed. The examples are very good and they demonstrate real world applications. ... Read more

Product Description

Customer Reviews (2)

a classic one
The book is just a classic piece of historical. It is probably not the best book on optimal control available, because of large progress since this seminal work was published, but anyone interested in optimal control should definitely consider spending that little money, just to have it.

A classic book on Dynamic Programming
It's a classic book on Dynamic Programming by its own creator, Richard Bellman. The mathematical models are always supported by good examples. However, the mathematical formalism is hold and quite different from what someone can find in the more modern references. ... Read more

Product Description
This major new volume provides business decisionmakers and analysts with a tool that provides a logical structure for understanding problems as well as a mathematical technique for solving them. The primary tool presented throughout Optimization for Profit is linear programming (LP)--a medium that can be mastered by any individual who seeks to improve his/her analytical and decisionmaking skills.

One of the special features of Optimization for Profit is the illustration of activity analysis as the technique used to formulate problems. By using activity analysis as the problem structure, linear programming become a natural extension of the way decision makers approach problems. As a result, linear programming becomes an integral part of the thinking process of the individual. Consequently, students or practitioners can readily create a linear programming model of an entire business or any part of a business. Several chapters are devoted to describing this technique and illustrating its application to many different types of companies, including an oil refinery, a marmalade production company, and a chicken processing plant. A thorough study of Optimization for Profit will enable you to work with any manufacturer or service industry and model all or part of the operation, and then solve the model to determine how best to minimize costs or maximize profits. Many firms save hundreds of thousands of dollars each year through the application of linear programming.

The authors have presented the material in this vital book so clearly and thoroughly that an individual could master the material through self-study. The inclusion of problems at the end of each chapter makes this book suitable as a textbook at the advanced undergraduate or beginning graduate level at most colleges or universities for students of management science, operations research personnel, and applied mathematicians working in industry, government, or academia.

Notable features of the book include:

• the practical aspects of modeling a business or any part of a business using linear programming
• a unique approach to explain the simplex method for solving linear programming problems
• real life, practical problems that are presented and solved in detail
• detailed instructions for those interested in solving linear programming problems on all types of computers from mainframes to PCs
• numerous problems provided for the benefit of the student and all of the linear programming models described in these problems as well as in the text itself are available on a diskette

Customer Reviews (1)

A very good guide in using LP in optimization problems
It's a great book for whoever is interested in linear programming applications to real world cases. From the introduction to the last chapter, the book provides a clear view of how linear programming works,how it can be applied, and what its advantages are. Lots of examples andexercises make this book a very good guide in using linear programming inoptimization problems. ... Read more

Product Description
Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableaus, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableaus the beautiful termination theorem of RG Bland is proven more simply than heretofore, and the important duality theorem becomes almost obvious. Examples and extensive discussions throughout the book provide insight into definitions, theorems, and applications. There is considerable informal discussion on how best to play matrix games.

The book is designed for a one-semester undergraduate course. Readers will need a degree of mathematical sophistication and general tools such as sets, functions, and summation notation. No single college course is a prerequisite, but most students will do better with some prior college mathematics. This thorough introduction to linear programming and game theory will impart a deep understanding of the material and also increase the student's mathematical maturity. ... Read more

Customer Reviews (1)

nice book
nice. very readable.
i would have liked it better if it treated convexity in a nicer manner and better displayed the underlying geometry, but it is very geared towards the applied side of things and this is good. (By "applied side", I do not mean it just lists formulas and procedures)
A rather good book. ... Read more

Product Description
COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED

Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.

Concentration on the three major parts of nonlinear programming is provided:

• Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming
• Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions
• Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems

Important features of the Third Edition include:

• New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more
• Updated discussion and new applications in each chapter
• Detailed numerical examples and graphical illustrations
• Essential coverage of modeling and formulating nonlinear programs
• Simple numerical problems
• Advanced theoretical exercises

The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems. ... Read more

Customer Reviews (3)

Excellent Text
This is a very good text for learning nonlinear programming. It expects that the reader has an understanding of linear algebra and mathematical sets but if you are prepared for a graduate NLP course then you'll find it accessible. It discusses how the problem formulation informs the type of algorithm best used to solve it as well as the algorithms themselves. As a graduate student, I highly recommend this book.

One of the best books on NLP at this level
I am also referring to the 2nd Edition of the book.

I largely agree with review by Marc Sachon except the part about Dantzig's book: if you are new to LP/NLP, or Mathematical Programming in general, stay away from Dantzig's book. Its writing style is entirely outdated and will put you to sleep in no time. Reading from Dantzig to learn about LP is like reading Newton's originals to learn physics/calculus.

If you're new to LP / NLP I *strongly* recommend Vanderbei, and THEN this book.

This book covers enough ground for fast paced novices and beyond novices.
It's mathematical but not rigorous in the strict mathematician's way - for that kind of exposure look elsewhere. It covers a breadth of subjects/issues related to LP / NLP not often found in other books at its level, so in a way it is like a small compendium.

It's more up-to-date than say, R. Fletcher's "Practical Methods of Optimization", or Gill, Murray & Wright's "Practical Optimization" both good MSc level books but somewhat dated now and perhaps a bit tedious sometimes. However, if you're a novice, I advise you to look at them also, if you have access to them, as they might serve your specific needs/ reading style better/equally well. You should also look at Luenberger's "Linear and Nonlinear Programming" which is also quite old but has a classic writing style and is holding up rather well. If you want the fine nitty-gritty details and the breadth of coverage though, Bazaraa has more. Luenberger's more solid and rigorous.

Haven't had the chance to look at the more recent "Nonlinear Optimization" byAndrzej Ruszczynski but it might be as good/better as he's also an expert in the field - so keep that in mind.

"Convex Optimization" by Stephen Boyd is more advanced (not too advanced though, depending on your maths ability) and moving in a slightly different field/teritory.

Great Book for NLP (for the mathematically inclined only!)
I am referring to the Bazaraa, Sherali and Shetty book "Nonlinear Programming, Theory and Applications", second edition (it seems that Amazon missed the third author).

This is a great book for anyone who isinterested in nonlinear optimization. The book presents the topic in aclear and concise manner, provides learning aides in form of examples andgenerally has a very well structured layout. I have other books on NLP, butI consider this the best one (Luenberger is great, too - but verycondensed). The book consists of three parts: the first part presentsconvex analysis, the second part looks at optimality conditions and thethird part presents algorithms. If you went through some OR textbooks andfelt that they didn't give you enough on NLP, this is the place to get yourfix!

This book for NLPs together with Dantzig's work on LPs and you havethe basic toolset for static optimization. ... Read more

Product Description
This text presents linear and nonlinear programming in an integrated setting and serves as a complete and unified introduction to applications, theory, and algorithms. ... Read more

Customer Reviews (4)

Bad presentation
This book explains linear programming concepts using tableaus. Tableaus are obsolete. If you want to solve a linear program, you use Maple, Mathematica, Matlab, GNU Octave or some other computer program. If you want to understand the simplex algorithm, you should study the linear algebra approach, and not tableaus.

The book is badly organized, the font is ugly and the theory is spread over zillions of examples. Definitions are hard find. The algorithms are presented in a very cumbersome manner. The exercises are so many you don't bother even to read them. I would be nicer with a few, carefully selected, exercises.

The book would not be nice for an introductory course since everything is presented in such an obfusacted way. For a second course, it's not useful either, since instead of solid theory it contains only the mentioned zillions of examples.

nothing special
the fact that none of the exercises have solutions is bothersome. i also had difficulty determining which ideas/equations have more emphasis than others. this book shouldn't be used as an introductory course due to its mediocre-at-best layout.

There are better books...
I found this book to be not so good for non linear programming. The notation is confusing and the discussion of subject itself is not organised. I prefer other books like the book by Bertsekas. I followed Bazaara's book for linear programming and hence I dont know about this book's linear programming.

clear
In my opininon it is more clear than the other examples of this category. But a deficiency for this book is there is no solutions to the problems as exercises. ... Read more

Product Description
This book introduces the applications, theory, and algorithms of linear and nonlinear optimization, with an emphasis on the practical aspects of the material. Its unique modular structure provides flexibility to accommodate the varying needs of instructors, students, and practitioners with different levels of sophistication in these topics. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines.

Part I of Linear and Nonlinear Optimization, Second Edition provides fundamentals that can be taught in whole or in part at the beginning of a course on either topic and then referred to as needed. Part II on linear programming and Part III on unconstrained optimization can be used together or separately, and Part IV on nonlinear optimization can be taught without having studied the material in Part II. In the preface the authors suggest course outlines that can be adjusted to the requirements of a particular course on both linear and nonlinear optimization, or to separate courses on these topics. Three appendices provide information on linear algebra, other fundamentals, and software packages for optimization problems. A supplemental website offers auxiliary data sets that are necessary for some of the exercises.

Audience: This book is primarily intended for use in linear and nonlinear optimization courses for advanced undergraduate and graduate students. It is also appropriate as a tutorial for researchers and practitioners who need to understand the modern algorithms of linear and nonlinear optimization to apply them to problems in science and engineering.

Contents: Preface; Part I: Basics; Chapter 1: Optimization Models; Chapter 2: Fundamentals of Optimization; Chapter 3: Representation of Linear Constraints; Part II: Linear Programming; Chapter 4: Geometry of Linear Programming; Chapter 5: The Simplex Method; Chapter 6: Duality and Sensitivity; Chapter 7: Enhancements of the Simplex Method; Chapter 8: Network Problems; Chapter 9: Computational Complexity of Linear Programming; Chapter 10: Interior-Point Methods of Linear Programming; Part III: Unconstrained Optimization; Chapter 11: Basics of Unconstrained Optimization; Chapter 12: Methods for Unconstrained Optimization; Chapter 13: Low-Storage Methods for Unconstrained Problems; Part IV: Nonlinear Optimization; Chapter 14: Optimality Conditions for Constrained Problems; Chapter 15: Feasible-Point Methods; Chapter 16: Penalty and Barrier Methods; Part V: Appendices; Appendix A: Topics from Linear Algebra; Appendix B: Other Fundamentals; Appendix C: Software; Bibliography; Index ... Read more

Product Description

Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.

Product Description

To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study.

—Choice Reviews

The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming.

—Mathematics of Computing

This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. After preliminary discussion of linear algebra and geometry, it describes the simplex algorithm, duality, the ellipsoid algorithm (Khachiyan’s algorithm) and Karmarkar’s algorithm.

—Zentralblatt Math

The exposition is clear and elementary; it also contains many exercises and illustrations.

—Mathematical Reviews

A self-contained, concise mathematical introduction to the theory of linear programming.

—Journal of Economic Literature

Product Description

The era of interior point methods (IPMs) was initiated by N. Karmarkar’s 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.

Product Description

This textbook for students and practitioners presents a practical approach to decomposition techniques in optimization. It provides an appropriate blend of theoretical background and practical applications in engineering and science, which makes the book interesting for practitioners, as well as engineering, operations research and applied economics graduate and postgraduate students. "Decomposition Techniques in Mathematical Programming" is based on clarifying, illustrative and computational examples and applications from electrical, mechanical, energy and civil engineering as well as applied mathematics and economics. It addresses decomposition in linear programming, mixed-integer linear programming, nonlinear programming, and mixed-integer nonlinear programming, and provides rigorous decomposition algorithms as well as heuristic ones. Practical applications are developed up to working algorithms that can be readily used. The theoretical background of the book is deep enough to be of interest to applied mathematicians. It includes end of chapter exercises and the solutions of the even numbered exercises are included as an appendix.