Book Description

The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications.The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables.The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions.Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference. ... Read more

Reviews (3)

first great treatment of generalized linear models
Nelder and Wedderburn wrote the seminal paper on generalized linear models in the 1970s. Since then John Nelder has pioneered the research and software development of the methods. This is the first of several excellent texts on generalized linear models. It illustrates how through the use of a link function many classical statistical models can be unified into one general form of model. This unification is helpful both theoretically and computationally. Various applications are presented in a clear manner.

Very comprehensive, very helpful.
The first edition is already a well-known text and reference, this expanded version is even better. Very comprehensive and very helpful.

One of the best books on modelling
This is an important book. It is a mature, deep introduction to generalized linear models.

General linear models extend multiple linear models to include cases in which the distribution of the dependent variable is part of the exponential family and the expected value of the dependent variable is a function of the linear predictor. Besides the normal (Gaussian) distribution, the binomial distribution, the Poisson distribution and the Gamma distribution, are just some of the exponential family members most frequently encountered in the scientific literature. Using appropriate functions to join the dependent variable to the linear predictor many classic models of applied statistics are included in the broad frame of generalized linear models: "logistic regression", log-linear models, Cox's proportional hazards models are just some of them.

Further extensions to the "base" family of generalized linear models, such as those based on the use of quasi-likelihood functions, and models in which both the expected value and the dispersion are function of a linear predictor, are well presented in the book.

Examples, and exercises, introduce many non-banal, useful, designs.

There are some minor drawbacks. Some more advanced topics might have been introduced more smoothly (i.e. conditional likelihood). Some other topics are better understood when you are already familiar with the specific object of study (i.e. Cox's proportional hazards models as a generalized linear model). The book does not provide software examples, nor is it related with any specific statistical package. However, the maturity of the reader to whom the book is addressed should be so high that translating the majority of the examples presented in the book in the "language" of a familiar statistical package should not be a problem. ... Read more

Book Description

Reviews (1)

Useful, but need solid background in stats
This book describes important advances in statistical analysis of social science data, circa 1992. Much of this data has a natural hierarchical grouping. But traditional statistical methods proved inadequate at coping. The biggest drawback was the failure of the assumption of independence. If at the lowest level, Items I1,...,In are grouped into sets J1,...,Jm, where mTo handle this, Hierarchical Linear Models were developed. The book gives a detailed treatment. A very comprehensive discussion. Including the handling of meta-analysis, where we wish to combine results across different studies. Which then involves using empirical Bayesian estimates. This method has also seen important usage in evaluating medical studies, conducted by different researchers on the same topic.

The book also illustrates the essential development of non-trivial computer programs to perform the gruntwork.

You will need a solid background in statistics to find this book useful. At a minimum, a year of statistics at the undergraduate level. ... Read more

Book Description

Designed to be accessible, this book develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving. This book features a collection of important topics from mathematics of finance, linear algebra, linear programming, probability, and statistics, with an emphasis on cross-discipline principles and practices. For the professional who wants to acquire essential mathematical tools for application in business, economics, and the life and social sciences.

Reviews (7)

Sound choice for a finite math textbook
This is a very sound choice as a textbook for a course in finite mathematics. The coverage is appropriate, the level suitable for the non-math major, the explanations are excellent and the authors take the title seriously.
The topics are covered in the following order:

* Elementary functions and their graphs.
* The mathematics of finance.
* Matrices and systems of linear equations.
* Linear inequalities and linear programming.
* Logic, set theory and basic counting.
* Probability and probability distributions.
* Basic game and decision theory.
* Markov chains.

There are many exercises and at the end of each section there is a set of basic exercises followed by a collection of applied problems. The set of applied problems is split into three categories: business & economics, life sciences and social sciences. Since finite mathematics is often a preparation for students to work in these fields, this format is what impressed me the most. With all of these "real world" problems to work as part of their study, no student using this book could ever legitimately say that they see no purpose to their studies. Solutions to the odd-numbered problems are included.
I came into contact with this book after my choice of textbook was irrevocable. Had I seen it earlier, it would have been the one I used.

Many exercises in economics, life and the social sciences
This is a very sound choice as a textbook for a course in finite mathematics. The coverage is appropriate, the level suitable for the non-math major, the explanations are excellent and the authors take the title seriously.
The topics are covered in the following order:

* Elementary functions and their graphs.
* The mathematics of finance.
* Matrices and systems of linear equations.
* Linear inequalities and linear programming.
* Logic, set theory and basic counting.
* Probability and probability distributions.
* Basic game and decision theory.
* Markov chains.

There are many exercises and at the end of each section there is a set of basic exercises followed by a collection of applied problems. The set of applied problems is split into three categories: business & economics, life sciences and social sciences. Since finite mathematics is often a preparation for students to work in these fields, this format is what impressed me the most. With all of these "real world" problems to work as part of their study, no student using this book could ever legitimately say that they see no purpose to their studies. Solutions to the odd-numbered problems are included.
I came into contact with this book after my choice of textbook was irrevocable. Had I seen it earlier, it would have been the one I used.

Not user friendly
I am currently using this book for my college course. Examples
are not clear, and many steps missed. Per our instructor alot of the answers in the back are inaccurate. I do not recommend this book for students whom are not well versed in algebra

This finite math book really counts!!
I recommend this book in a heartbeat to anyone taking an introductory college-level mathematics course. I've used this book in courses that I've taught and students love it! Yes, there is a lot of material, but no, who says you have to read every page? It is also a great mathematics refresher! Furthermore, it covers many aspects of the mathematics of finance.

Excellent Text!
I sinmply loved the flow of this text! It mader so much sense to me the way the book went from one concept to the other! Highly recommended if you want to really learn and not "slide" through. ... Read more

Book Description

A complete, highly accessible introduction to one of today's most exciting areas of applied mathematics

One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade.

Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include:
* Network flow problems
* Optimal matching
* Integrality of polyhedra
* Matroids
* NP-completeness

Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come. ... Read more

Reviews (3)

A Classic in Combinatorial Optimization
Combinaorial Optimization is one of those rare books that is an instant classic. The authors weave a readable fabric of intuition and theory that is unmatched in this exciting discipline. The choice of topics covered begins with two fundamental optimization problems, namely, the minimum spanning tree and shortest path problems. Next, maximum flow and minimum cost flow problems are discussed, followed by matching problems, polyhedral issues arising in combinatorial optimization, and the famous traveling salesman problem. The text concludes with chapters on matroids and NP-Completeness. The exposition on these topics is very well written and the proofs are rigorous. There is a terrific blend of theory, algorithms and applications without overwhelming the reader with computational details. The authors also do a good job of developing an accurate historical perspective of the material, most of which evolved during the time period 1955 to 1995. The book is suitable for an upper-level undergraduate, or a graduate course. The exercises are very well thought out and are at an appropriate level. I have taught undergraduate courses in combinatorial optimization for over 10 years and have always struggled to find an appropriate text. My problem has now been solved.

Elegant one, but not a lot of details.
This book was thoroughly written by great-minded Masters. It is well-organized in their topics and presentation. However, the book details is unbalnced, some chapters are overwhelm the data, and some others are insufficient. By the way, I graded this book a Very Good one. Worth Reading !!

A superb introduction to Combinatorial Optimisation
A good introduction to Combinatorial optimisation and integer programming.

Especially recommended are the chapters on minimum weight matching and the TSP. ... Read more

Book Description

Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.
· Comprehensive coverage of this growing area of research
· Carefully introduces each algorithm with examples and in-depth discussion
· Includes many applications to real-world problems, including engineering design and scheduling
· Includes discussion of advanced topics and future research
· Can be used as a course text or for self-study
· Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms
The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study. ... Read more

Reviews (2)

Great book; a must for engineers and scientists alike
Kalyanmoy Deb has put together a great summary of the state of affairs in multiobjective genetic algorithms. Should you be an engineer or a scientist involved in the optimization of any design of sizeable complexity, you should read this book and become familiar with the techniques that have evolved over the last decade into powerful methods of optimization. This book is in many many ways bridging the gap from Michalewicz's and Fogel's book ("How to solve it") to the more modern era of this field (eg late nineties up to now...). So whereas those two authors never really considered multiobjective genetic algorithms, Deb plows through with the great expertize of a (perhaps even "the") leading researcher in that domain. This is a great book of _receipes_ with the level of details necessary to make use of them. It's a "how to" book; this is the one you have cracked open on your desk while you're hard coding it all up. However, it's not very well written with the prose being very terse and basically quite unengaging. But so what! In some sense yes perhaps, but Michalewicz and Fogel made a point that one can write technical litterature that one can also read. Perhaps they went overboard... in any case, Deb's book is about algorithms so who cares about whether the book puts you to sleep and it can do that, unfortunately. Apart from the unengaging style and the paucity of depth in the examples scope, the real problem with the book is not with the book itself, it's with the field of multiobjective optimization based on evolutionary methods. It's fairly evident that there is not much of any sort of fundamental understanding available at this time in support of why evolutionary techniques do work well, and they do, sometimes... If this understanding is available, you won't find it in Deb's book. If you are like me though, you won't care all that much really so long as the techniques are efficient and presented in a way that make them useable, and that's done right... But on the whole, it's a little unsatisfying because one's left with a panoply of various techniques and ways to define operators and representations but there is no insight given on which one might be best or how to craft them to particular situations. There is a lot of so-'n-so in reference this and that did it like this and it seems to work well there, however... The reason for this state of affairs is, of course, that nobody has a real clue, yet... But that is _not_ Deb's fault and this is not why, as a user, I'm not rating his book a full 5 stars. In some sense it could be rated as high as that but I thought the presentation was rather unengaging and not with all the breath and depth it could have had. So it's a 4.5 stars perhaps... let's say... but Amazon does not let me select 4.5 stars so it's 4, this edition at least...

The Reference in Evolutionary Multiobjective Optimization
This is the first complete and updated text on Multi-objective Evolutionary Algorithms (MOEAs), covering all major areas clearly, thoughtfully and thoroughly. Thanks to the development of evolutionary computation MOEAs are now a well established technique for multi-objective optimization that finds multiple effective solutions in a single run. The widely interdisciplinary interest of engineers, scientists and mathematicians towards MOEAs has been evident during the first international conference on this topic (EMO2001,Zurich). The book is extremely useful for researchers working on multi-objective optimization in all branches of engineering and sciences, that will find a complete description of all available methodologies, starting from a detailed description and criticism of classical methods, towards a deep treating of the most advanced evolutionary techniques. Moreover several analytical test cases are given, covering all difficulties a MOEA encounters when converging towards the Pareto Optimal front. This set of test problems, together with several performance measurement parameters are essential when testing a new strategy before its application to a real-world problem. Despite the detail in advanced topics, Deb's book may be also used as a reference-book for a post-graduate course thanks to the scholarly coverage of basic arguments. As a final remark I strongly suggest everyone working on evolutionary computation and optimization to keep this book on the desk. ... Read more

Book Description

This book is specifically designed to change the way deterministic optimization is taught to introductory students.Toward this end, it exposes students to the broad scope of the topic,reinforces the basic principles, sparks students' enthusiasm about the field, provides tools of immediate relevance and develops the skills necessary to use those tools. ... Read more

Reviews (12)

Excellent book
This is an excellent book for those who need to use the power of operations research methods (esp the newer algorithms, interior point methods etc.) but dont have the time to chew on pages of theory. Must congratulate the author on a job well done. Is it possible to bring out a cheaper paper back edition ? That would benefit the student and research community immensely.

This book is very clear and easier to read and understand.
In my work I needed to find the shortest path from a single point to a set of points. This book really helped me to find the suitable method: the Dijkstra algorithm. I began reading Chapter 9, which is "Shortest Paths and Discrete Dynamic Programming". The material is presented clearly and with relevant and adequate variety of examples. I haven't read the other chapters since they are not required for my work at this moment and I don't have ample time to make a full review; however, I can say this: My many years in research in several fields have often put me in a position of transfering mathematical algorithms in one field to another or to search for an effecient one. I frequently get a limited time period to do literature search and I usually page-read many books. This is one of the rare books which are easy to read and comprehend. I thank and congratulate the author for doing a wonderful service.

PhD student in IE
If you are taking a graduate or an undergraduate course in OR, this book is a must! I have not seen ANY book able to present OR with such simple, direct examples and WITHOUT sacrificing theory.
This is the best written textbook I have ever read. When I compare it with the hundereds of dollars I spend on badly written books, even as a PG (poor graduate) student I would gladly pay twice of what this book is priced at.

Awesome
after all he is from Purdue!! and I am his current student in the operation research course. he is awesome and the book is awesome..

thanks

The BEST, easy to understand OR / Linear Prog. book!
I got my B.S.E. in Industrial & OPS Eng. from U of Michigan. During that time, I had to take a course in Linear/Math. Programming. The course content was simple, but the book we used was TERRIBLE!!. Now finishing my M.S., I used this book in an OR class for my Masters Prog, and it is THE BEST BOOK! I literally read it page by page. It is the best written, hand holding book to a rather complicated subject. I got an A in the class, and gained great understanding. This is a book I WILL KEEP FOREVER, a great reference for the workplace as well!!! ... 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

Reviews (2)

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 historical notes about the history of both linear and integer programming.

It is the first book, both me and my advisor check out, when we require any thing on Linear and Integer Programming. ... Read more

Book Description

This book is the only source that provides comprehensive, current, and correct information on problem solving using modern heuristics. It covers classic methods of optimization, including dynamic programming, the simplex method, and gradient techniques, as well as recent innovations such as simulated annealing, tabu search, and evolutionary computation. Integrated into the discourse is a series of problems and puzzles to challenge the reader. The book is written in a lively, engaging style and is intended for students and practitioners alike. Anyone who reads and understands the material in the book will be armed with the most powerful problem solving tools currently known.

This second edition contains two new chapters, one on coevolutionary systems and one on multicriterial decision-making. Also some new puzzles are added and various subchapters are revised.

Reviews (9)

extremely well written
I read this book while taking an advanced class in heuristics. I found the book to be extremely well written and very compelling to read. Although dealing with advanced topics, the authors' friendly and clear writing style makes it accessible to anyone with a CS background.

The first half of the book is on search heuristics, covering methods such as traditional searches (exhaustive search, greedy algorithms, divide and conquer, dynamic programming, A*, etc), methods to escape local optima (simulated annealing, tabu search), and, perhaps most interesting of all, evolutionary algorithms. I later found out that these topics are typically taught in undergraduate artificial intelligence courses, an elective I never took. The second half of the book covers even more advanced areas, such as contraint-handling, neural networks, and fuzzy systems.

The authors use three recurring example applications to demonstrate each search technique: the boolean satisfiability problem (SAT), travelling salesman (TSP), and a nonlinear programming problem (NLP). I really liked the consistent use of these three examples, as they give a sense of continuity throughout the book that helps the reader compare search techniques clearly. I had of course studied the TSP problem in my undergraduate algorithms class but neverin the context of such interesting approximation algorithms. In my heuristics class we had assignments to implement the TSP search problem using the Lin-Kernighan method, dynamic programming, and an evolutionary algorithm.

The written English in this book is simply outstanding and crystal-clear, which was something of a shock since I was unable to even pronounce the first author's name. The writing is in a very friendly tone with elements of humour dispersed throughout. Interestingly, in the summary chapter, there is an anecdote on the 1980s TV show Magnum PI (I even remember the mentioned scene myself), further revealing the friendly, plain-English tone of the book. Perhaps the best part of the book is that the numerical mathematical discourse is kept at a minimum (used largely for the NLP problems), so people who haven't taken calculus in ages (like me) can easily enjoy the book.

As an added bonus(!), between each chapter is a brain-teaser problem like those found in those legendary Microsoft interview questions.

My only complaint is that there is no simple analysis of the running time complexity of each algorithm, which even in its simplest form would have been a great thing to read about.

In summary, this book is an excellent read if you enjoy the topics covered. Highly recommended.

Fine-tuning to common sense
Beside the great ideas provided in this book for problem solving, it provides a deep wisdom of for piecing some of the puzzles of our life. I recommend it.

Useful overview of methods
I first ordered this book thinking it was George Polya 's book "How to solve it", then I realized it wasn't and I bought it anyway since I thought it might turn out as a "must read" book, just like Polys'a book.

One one hand it was a dissapointment, because the books are not written in the same manner and don't attact similar problelsm.

But then, this book makes you look into problems, and realize that usually we people are usually good in solving problems of the sort we learned how to (well... duh!), but surprisingly, we have a hard time solving even trivial problems if they are not placed in the context we got used to seeing them.

This book comes and tries to make things better in this department, showing you some general methods for solving problems, and also showing problems and suggested solutions along with a long discussion.

You should be able, once you've read the book and put your mind to it, to be better in understanding problems, understanding which tool to use for solving them and finally, understanding the tools enough to be able to actually solve the problem.

I enjoyed the overview of methods, and there are many such methods throughout the book (perhaps a complementary book for learning which "machine learning" methods are available these days and what sorts of problems they are useful for solving would be Tom Mitchell's "Machine Learning" book).

I wasn't sorry for buying this book. I'm happy I was fortunate enough to bump into it.

Makes spinach taste good
I am a computer scientist, but have gotten impatient over the years with the needless formalization that occurs in algorithmic texts. This is a delightful breath of fresh air in terms of balancing erudition with attempts to be "user friendly". If you want the latest and greatest twist to a well known technique, this book won't provide it. But it does a great job of competently and lucidly explaining the value proposition behind each optimization method and how to gradually upgrade from applying it naively to the more intricately optimized applications. Well done!

Must buy...
Clearly this is an outstanding book. It takes the reader close to the current knowledge frontier in the domain of heuristics of optimization. The style is educational and the prose supports it. That is probably the reason why everyone rates the book so high. However, it does have a downside: multiple (or reference) readings are not as easy. What helped for the first reading gets in the way for the others. Oh well... Can't really win, can you?

The references are ample and very detailed. That is necessary because some of the treatment (not all, by any means) israther descriptive sometimes and will necessitate looking them up and some references (not all, by any means) may not be easy to find (you'll be the judge...). Also, if you are looking for up-to-date treatment of multiobjective GA's, you won't find it there because, well, the field has already evolved.

So, overall, this is a "must buy" book and you will not have to take on a second morgage to purchase it. That's good! ... Read more

Book Description

Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensionalmodels of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods.

Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

This new edition includes a wide range of the best methods available today. The author has added a new chapter on multigrid techniques and has updated material throughout the text, particularly the chapters on sparse matrices, Krylov subspace methods, preconditioning techniques, and parallel preconditioners. Material on older topics has been removed or shortened, numerous exercises have been added, and many typographical errors have been corrected.The updated and expanded bibliography now includes more recent works emphasizing new and important research topics in this field.

Audience
This book can be used to teach graduate-level courses on iterative methods for linear systems. Engineers and mathematicians will find its contents easily accessible, and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science.

Contents
Preface to the Second Edition; Preface to the First Edition; Chapter 1: Background in Linear Algebra; Chapter 2: Discretization of Partial Differential Equations; Chapter 3: Sparse Matrices; Chapter 4: Basic Iterative Methods; Chapter 5: Projection Methods; Chapter 6: Krylov Subspace Methods, Part I; Chapter 7: Krylov Subspace Methods, Part II; Chapter 8: Methods Related to the Normal Equations; Chapter 9: Preconditioned Iterations; Chapter 10: Preconditioning Techniques; Chapter 11: Parallel Implementations; Chapter 12: Parallel Preconditioners; Chapter 13: Multigrid Methods; Chapter 14: Domain Decomposition Methods; Bibliography; Index. ... Read more

Reviews (1)

Great Book
This is a great book for this subject. The book is easy to follow and Saad does a wonderful job of illustrating with examples. This is a great textbook or a book for reference. This book does a particularly good job with Krylov methods and does a reasonable job with preconditioning. ... Read more

Book Description

This book introduces students to optimization theory and its use in economics and allied disciplines.The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified.The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming.A preliminary chapter and three appendices are designed to keep the book mathematically self-contained. ... Read more

Reviews (5)

The title says it all
A first course in Optimization theory - that is what the book is. The target audience is those who are inetersted in the theory of optimization. Some familiarity with Mathematical Analysis and Matrix Algebra would be helpful; however the first chapter lays the mathematical foundation and a careful reading would enable the reader to tackle the rest of the book.

Previous reviews have made a chapter by chapter analysis of the book and hence I will just highlight some of the things I liked about the approach used by the author. Whenever a theorem is stated different examples are given to emphasize the points. For example when stating the Lagrange Theorem and Kuhn-Tucker theorem the author points out when the theorems fail and gives detailed examples to illustrate the ideas. The author often draws from examples in finance to illustrate the practical importance of the theory. The one I liked most was how a cost minimization problem was solved by reducing the solution space to a compact space and then applying the Weierstrass theorem. The author also shows how some of the "cookbook" procedures really work and warns the readers against potential pitfalls in applying such procedures. If you are planning to study optimization theory and are looking for a good entry point into the subject this book is for you.

Good introduction to the field of optimization
This book gives a nice introduction to the theory of optimization from a purely mathematical standpoint. The computational and algorithmic aspects of the subject are not treated, with emphasis instead placed on existencetheorems for various optimization problems. The author does an effective job of detailing the mathematical formalism needed in optimization theory. After a brief review of background mathematics in the first chapter, the author outlines the objectives of optimization theory in Chapter Two. He also gives some examples of optimization problems, such as utility maximization, expenditure minimization, profit maximization, cost minimization, and portfolio choice. All of these examples are extremely important in industrial, logistical, and financial applications. The author is also careful in this chapter to outline his intentions in later chapters, namely, that of finding the existence of solutions to optimization problems, and also in the characterization of the set of optimal points. The existence question is outlined in Chapter Three using only elementary calculus, and the Weierstrass theorem is proved. Necessary conditions for unconstrained optima are examined in the next chapter, again using only elementary calculus and linear algebra. Lagrange multipliers and how they are used in constrained optimization problems are effectively discussed in Chapter 5. To discuss how optimization problems vary with a set of parameters, in particular if they vary continuously with the set of parameters, the author introduces the concept of a corespondence. This is essentially a map that assigns sets to points. His discussion of upper and lower-semicontinuity is very clear and I think one of the best presentations given at this level. He then proves a maximum theorem, showing that parametrized optimization problems can have continuous solutions under certain conditions. A game-theoretic application follows along with statements, but not proofs, of the Kakutani and Brouwer Fixed Point theorems. The author introduces an order relation on the parameter space and discusses parametric monotonicity in the next chapter. Again a game theory application is given along with a statement (but not a proof) of the Tarski Fixed Point theorem. The last two chapters cover dynamic programming and these are the most interesting chapters of the book. It is here that the author makes the connection with more advanced treatments of optimization theory, via Banach spaces and nonlinear functional analysis. With further reading in real analysis and topology, readers will be well on their way to understanding more advanced treatments of optimization theory that use nonlinear functional analysis and differential topology.

Unless you're into theory, this book is NOT for you
I'm a applied mathematician with over 40 quarter hours of theoretical math under my belt, and frankly I feel this book would be rough going for anyone who does not have a rigid math theory background. In other words, if you're not a graduate student or a theoretical practioner in the field of optimization, this is NOT the book for you (most likely). But I also have two other problems with this book.

First, it is touted to have numerious examples of both theory and applications. Theory, as I mentioned above, it has in abundance. But it is very thin on practical applications.

Second, this book has numerious problems at the ends of the chapters WITH NONE OF THEM WORKED OUT! Frankly, I'm not really interested in paying almost $30 for a paperback book that is unfinished.

Perhaps I was expecting much more than what I got after reading the glowing reviews above; and in hindsight, I really should have paid more attention to the title as "Theory" is indeed the operative word. My irritation is not in the book itself, as the author states in his forward that he is writing a book aimed the graduate school set; but is aimed at the reviewers above which led me to think that this text was much wider based than it turned out to be.

Great book and an even greater value
This book was organized and written with perfection. The explanations are remarkable and the "cookbook" procedures for Lagrange and K-T methods were great. I especially admired the fact that the author actually mentioned how these procedures could fail to yield an optimized value. This is worthwhile in today's university mathematics where one is simply taught to plug numbers into formulae and algorithms to get the desired answer. The book also slants towards optimization problems in economic theory as well as other disciplines. Finally, in an age when textbooks can easily run over $100, it was nice to see this book, filled with a wealth of information, so moderately priced.

Excellent book for PhD students in Operations Management
This is an excellent book for anybody interested in non-linear optimization within economics framework. The book is self-contained and includes all the basic theory one needs to know to understand optimization. To my knowledge, this is the only book merging non-linear optimization with game theory and such concepts as supermodularity and parametric monotonicity. ... Read more

Book Description

Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book. ... Read more

Reviews (4)

Simply the perfect math book
Optimization by Vector Space Methods, by David Luenberger, is one of the finest math texts I have ever read, and I've read hundreds. Many years ago this book sparked my interest in optimization and convinced me that the abstract mathematics I had been immersed in actually would be applicable to real problems. Since then, Luenberger's book has inspired several of my graduate students. I merely lent them my copy, and Luenberger did the rest; he drew them in by carefully laying the foundation for an elegant theory, with just the right mix of formalism and intuition, and opened their eyes to the beauty and practicality of abstract mathematics. Anyone with an interest in higher-level mathematics (beyond multi-variable calculus, say) would benefit from exposure to this finely-crafted book. I daresay, the rampant math anxiety that is so prevalent in the West would be substantially reduced if more authors would take such meticulous care in presenting their material.

The format of Luenberger's book is also extremely appealing in a way that I cannot quite put my finger on. The typography and illustrations are inherently crisp and inviting; they draw you in. There is nothing at all superfluous or gratuitous in this book. It is utterly to-the-point, methodical, and above all, clear. The techniques are developed starting from an elementary treatment of vector spaces, then proceeding on to Banach spaces and Hilbert spaces. Along the way, Luenberger introduces convexity, cones, basic topology, random variables, minimum-variance estimators, and least squares, among many other things. There is a recurring theme of duality, which can be used in a way analogous to the inner product of a Hilbert space. In particular, the familiar projection theorems of Hilbert spaces can be echoed in simpler normed linear spaces using duality, which Luenberger motivates and covers beautifully.

The book also covers some of the standard fare of functional analysis, such as the Han-Banach theorem, strong and weak convergence, and the Banach inverse theorem. However, Luenberger never wanders too far off into abstract nonsense; around every corner lay tantalizing application of these ideas to optimization. Luenberger first explores optimization of functionals then covers constrained optimization, which builds upon concepts such as positive cones and Lagrange multipliers. The optimization methods themselves have endless applications in fields such as computer vision, computer graphics, economics, and physics. Indeed, the list is effectively endless as optimization techniques pervade math and science.

I'm certain that the appeal of this book is helped immeasurably by the inherent beauty of the subject matter. Hilbert-space methods are lovely in themselves--they possess a structure that engages one's geometric intuition while at the same time admitting convenient algebraic properties. Once you are in the habit of phrasing problems in abstract settings such as Hilbert spaces, it forever changes how you look at things; you cannot help but look past the clutter to the essence of a problem (or, at least try very hard to do so). While this material is not nearly as abstract as, say, category theory, it nevertheless hits a high point in mathematics--a point more people ought to experience.

If you've had some exposure to optimization methods, or need to apply them in the context of computer vision, graphics, or finance, to mention just a few areas, then I urge you to take a look at Luenberger's fine book. It too hits a high point in clarity of mathematical writing. Combine beautiful theory with endless applications and lucid writing, and you have a winner of a book.

Thank You Dr. Luenberger
I owe Dr Luenberger a million thanks for writing this book. As his student, I think he is the master of putting complex issues in simple words. Your faithful student..Jayanth Krishnan

An alternative introduction to functional analysis
When I decided to change my career path from B-school to mathematics, I know that only with taking calculus and linear algebra courses is definitely not enough for me to get into a decent math graduate program. I spent an afternoon in a local bookstore to find a book for functional analysis and Hilbert space which is comprehensible for me at that time. I found Luenberger. I was obsessed with its clarity and simplicity without sacrificing too much rigor. Especially for those finance student who want to learn some advanced math for quant finance but may not have enough background to deal with, Luenberger's book is a really good starting point!

Top Secret: a pedagogic powerhouse for the confused
A few years ago, when I was a student first coming into contact with Hilbert spaces, linear operators, etc., I was absolutely confused by conventional textbooks. Hopelessly lost, an old friend from Cornell let me in on a little secret: Luenberger. Apparently, every student at his department was "secretly" reading this book on the side in order to get that elusive commodity -- "clear understanding" -- at which Luenberger is an absolute master.

I took my friend up on his suggestion, and it was a revelation. I was amazed. I was also furious at the fact that my professor had not assigned this book to us. After confronting him with it, he admitted that not only was he very familiar with it, it had also been instrumental for him when HE was a student. It seems Luenberger has been a "secret" text that students have been using for a generation or so.

Recently, when speaking with a confused and discouraged student, I let him in on it: "Luenberger. Forget everything else for now, and just work through Luenberger". A few days later, he came back and furiously confronted me as to why I did not recommend this to him beforehand...etc.

..and the legacy continues.

Dr Luenberger, thank you very, very much! ... Read more

Book Description

AMPL is a language for large-scale optimization and mathematical programming problems in production, distribution, blending, scheduling, and many other applications. Combining familiar algebraic notation and a powerful interactive command environment, AMPL makes it easy to create models, use a wide variety of solvers, and examine solutions. Though flexible and convenient for rapid prototyping and development of models, AMPL also offers the speed and generality needed for repeated large-scale production runs. This book, written by the creators of AMPL, is a complete guide for modelers at all levels of experience. It begins with a tutorial on widely used linear programming models, and presents all of AMPL's features for linear programming with extensive examples. Additional chapters cover network, nonlinear, piecewise-linear, and integer programming; database and spreadsheet interactions; and command scripts. Most chapters include exercises. Download free versions of AMPL and several solvers from www.ampl.com for experimentation, evaluation, and education. The Web site also lists vendors of the commercial version of AMPL and numerous solvers. ... Read more

Reviews (2)

BEST MODELING LANGUAGE IN THE WORLD
Creative
Clear
Consistent
Cost little

A Great Companion for Great Software
Most software "companions" (more than a manual...not quite a book) really do not do justice to the software. Quite the contrary for the AMPL guide. AMPL (the language) is a *very* powerful and *very* easy to use Optimization package. It interfaces with most of the major solvers. Users program in AMPL which is more or less pseudocode and then solve LP, nonlinear, combinatorial, integer, etc. programs. Unlike most software packages, it is both robust and easy to use. Likewise with the companion/book. There are many great, easy to follow examples, and it clearly explains the intrecacies of the language. A must use software and most own book for anyone doing any optimization work. ... 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. ... Read more

Book Description

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems.With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis.Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed. ... Read more

Book Description

NUMERICAL OPTIMIZATION presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available.

Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the area.

Above all, the authors have strived to produce a text that is pleasant to read, informative and rigorous--one that reveals both the beautiful nature of the discipline and its practical side. ... Read more

Reviews (2)

Teaches good mathematical programming techniques
The book does a very good job in teaching non-discrete mathematical programming techniques. But, it is not an introductory book. The reader is supposed to know linear algebra and numerical analysis to a certain extent. Most of the modern techniques are presented, but the layout is a little chaotic- the sequence of subjects could be made better. So, I would have preferred to give it 4.5 stars (which is impossible). However, that does not take away the fact that the book is excellent. I have used it primarily for modelling financial portfolios, and I am sure it can be used as a guide for other applications.

Conclusion: A little difficult, but well worth the time and money involved

Nice but could be better!
This book by Nocedal and Wright has several attractive features. For one, it is probably the most "state-of-the-art" of the existing texts in optimization and as such covers most of the modern methods. It also has a nice section on LP (simplex as well as interior point methods) for someone interested in a course on optimization as opposed to NONLINEAR optimization (which is what I was looking for). Another strength is that it covers many of the algebra-related details very well. My only major complaint is that it seems to not get into any of the methods designed specifically for convex programs - these while admittedly less general are often very powerful. For example, there is NO mention even of Geometric Programming which has wide application in design. The convex simplex method also isn't mentioned anywhere. Finally,I wonder why there is no mention of the generalized reduced gradient (GRG) method.

All in all, a good book to own I think... ... 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 edition of this book and the second edition expands and further illustrates this relationship.Linear and Nonlinear Programming covers the central concepts of practical optimization techniques. It is designed for either self-study by professionals or classroom work at the undergraduate or graduate level for technical students. Like the field of optimization itself, which involves many classical disciplines, the book should be useful to system analysts, operations researchers, numerical analysts, management scientists, and other specialists from the host of disciplines from which practical optimization applications are drawn. ... Read more

Reviews (3)

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 from matematicians for matematicians. Hence it is quite hard for engineers both to read and to extract valuable information from them. With this respect this book is a shining star. It presents the topics in a very precise but clear and understandable way. Moreover the notation also is the best compromise between coinciseness and clarity. Matematicians, please, look at this book and follow such style; we engineer desperately need to communicate 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 Interior Point Algorithms and to tell you the truth why should he? I do not know other editions but in the first edition in chapter 7 "Basic Descent Methods" everyone who is able to read clearly and unbiased the second paragraph will agree with me that Interion Point Algorithms IS NOTHING NEW in the theory of MATHEMATICS!!! What you need to know ,the magic, is in the chapters 7-11. From there you can read everything else you like and get in touch with what is about to come in the next 25 years(See Ye : "Interion Point Algorithms"). But remember you are already in stars 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

Presents recent developments of key topics in nonlinear programming using a logical and self-contained format. Divided into three sections that deal with convex analysis, optimality conditions and duality, computational techniques. Precise statements of algorithms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations and numerous exercises to aid readers in understanding the concepts and methods discussed. ... Read more

Reviews (1)

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 is interested in no