Book Description

This book is a concise account of convex analysis, its applications and extensions, for a broad audience.Blurring as it does the distinctions between mathematical optimization and modern analysis, the elegant language of convexity and duality is indispensible both in computational optimization and for understanding variational properties of functions and multifunctions.Primarily aimed at first-year graduate students, the text consists of short, self-contained sections, each followed by an extensive set of exercises, many of which are guided.The book is thus appropriate either as a class text or for self-study. ... Read more

Book Description

This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students. ... Read more

Book Description

This volume presents a particular aspect of control theory-stabilization of programmed motion. Methods of the construction and synthesis of stabilizing controls are introduced together with original results and useful examples. The problem of optimal stabilization control synthesis is solved for linear systems of difference equations with quadratic quality criterion. ... Read more

Reviews (4)

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

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

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

The best book on Linear Programming I've ever come across.
A masterpiece on Linear Programming. Although it does not contain Interior Point Methods developed subsequently, it's always the first book I refer to, whenever I have any questions on Linear Programming. Strongly Recommended.

Good Book. Highly Recommended.
This book is a good introduction to linear programming. And very readable. It also serves as a good reference. For a more advanced text and non-linear programming topics, look at Nash and Sofer. ... Read more

Book Description

Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria. Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine. Thus, the question `Which is the best method for a given problem?' has become one of the most important and challenging ones.This is exactly what this book has as its focus and why it is important. The author extensively compares, both theoretically and empirically, real-life MCDM issues and makes the reader aware of quite a number of surprising `abnormalities' with some of these methods. What makes this book so valuable and different is that even though the analyses are rigorous, the results can be understood even by the non-specialist.

Audience: Researchers, practitioners, and students; it can be used as a textbook for senior undergraduate or graduate courses in business and engineering. ... Read more

Reviews (6)

A comprehensive study on AHP and other popular MCDM methods
This is a very good book for people who are involved in evaluating different alternatives and each alternative has its own strengths and weaknesses. It is also a very good reference for students and researchers who are studying/working in the area of decision analysis. It is especially useful for people who are interested in trying to find out which MCDM method is the best and who have used or intend to use the AHP method in their work or research. It has extensive and intensive coverage on the AHP method for ranking alternatives, other pairwise comparison methods for extracting weights, their shortcomings and improvement, and their comparisons with other popular MCDM methods. The discussions on the ranking abnormalities of the AHP method and its revised versions are very informative. The comparisons are supported using numerous numerical examples, the conclusions are convincing, and the contents easy to understand.

A must-read for practioners and researchers. Excellent!
I read this book with great interest. I am a Faculty Member at the New York University. This book is very clear to the point. I liked very much the in-depth analyses of many real-life MCDM issues and also the many numerical examples. The computational results are very thorough and revealing. The first book of its kind. An Excellent piece of work!!!

Comments from Dr. E. Triantaphyllou, email: trianta@lsu.edu
Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas during at least the last two decades. Thus, due to the importance of this field, many MCDM methods have been proposed. Ironically, often these methods contradict each other when they are posed to solve the same decision problem. This, in turn, has increased the confusion in MCDM theory and practice.

As Professor H.-J. Zimmermann from Aachen, Germany, remarked in the foreword for this book, this is exactly where this book has its focus and why it is that important: Rather than suggesting another MCDM method without any convincing justification, this book concentrates on the best known and most frequently used methods, compares them extensively and makes the reader aware of quite a number of "abnormalities" of some of the methods of which users are often not conscious. The book also considers very critically the most touchy points in solving real MCDM problems, namely, the quantification of qualitative data, how to derive relative weights of importance from ratio and difference comparisons, and also how to perform a sensitivity analysis with many MCDM methods.

This book provides a unique perspective into the core of MCDM methods and practice. Many theoretical and empirical analyses are presented and are complementary to each other. This allows the reader to gain a deep theoretical and practical insight into the topics covered in this book. In addition, the author offers at the end of each chapter and at the end of the book suggestions for further research. More information on this book can be found in the personal web site of the author which is located at the Louisiana State University in the U.S.A.

A nice book!
I enjoyed reading it! Nice exposition of the various subjects.

A must-read for practioners and researchers. Excellent!
I read this book with great interest. I am a Faculty Member at the New York University. This book is very clear and to the point. I liked very much the in-depth analyses of many real-life MCDM issues and also the many numerical examples. The computational results are very thorough and revealing. The first book of its kind. An Excellent piece of work!!! ... Read more

Book Description

The discrete Volterra series holds particular value in the analysis of nonlinear systems in telecommunications. However, most books on the Volterra series either do not address this application or only offer a partial discussion. Nonlinear Aspects of Telecommunications provides an in-depth treatment of the Volterra series and the benefits it offers as a representation of nonlinear problems, particularly in echo cancellation in digital telecommunications systems.Beginning with the fundamentals of the discrete Volterra series, the author presents its basic definition, notions, conditions for convergence and stability, and its matrix representation for multiple-input and multiple-output nonlinear digital systems. He pays significant attention to the important problem of approximating a nonlinear digital system using the discrete Volterra series and offers new results in this area--results not yet available in other texts.The second part of the book uses the background of Part I to show the Volterra series' application to echo cancellation. It provides introductory material regarding the basics of adaptive cancellers, and analyzes structures for nonlinear echo cancellers using nonlinear transversal filters for baseband transmission. The last section covers nonlinear echo cancellers for voiceband transmission and interleaved structures.Full of illustrations, examples, and new results, Nonlinear Aspects of Telecommunications is your first and best resource for understanding and applying the discrete Volterra series to nonlinear echo cancellation problems.Features ... Read more

Book Description

This work brings together some of the most up to date research in the application of operations research and mathematical modeling techniques to supply chain management problems. The book's chapters place a heavy emphasis on the application of modeling techniques to real world management problems. Each chapter is a self-contained study of a timely and relevant research problem in supply chain management. In many instances, the actual results from applying these techniques in practice are highlighted. In addition, each chapter provides important managerial insights that apply to general supply chain management practice. Included are several chapters that address the new and rapidly growing role of eCommerce in supply chain management.

Audience: This book can serve as a valuable reference for researchers in supply chain management as well as a reference textbook for a graduate level reading course. ... Read more

Book Description

Exceptionally practical, itfeatures several chapters that present new techniques and methodologies in thecontext of real-life problem situations.Broad andcomprehensive in coverage — and reader-friendly in approach, this bookfocuses on the most modern skills available for the design, operation andevaluation of civil and environmental engineering systems, optimization/systemsmodeling and engineering economics. Describes how and why linear programmingworks. Also, provides a solid treatment of multiple objective programming. Practicing Civil and Environmental Engineers. ... Read more

Reviews (2)

great book
The text is an excellent introduction to the world of civil engineering from a systems perspective. The goal is to introduce the tools and methods of systems analysis for the civil or environmental engineer. Applications are provided to illustrate the concepts.

Very well done from start to finish.

I've seen better
This was the text book I used my senior year in college for an wastewater engineering class. The reading material does not explain the subject and the example problems included in the chapters are not useful. The questions at the end of the chapters are excellent test material but can not be solved by understanding the material within the chapter. ... Read more

Book Description

Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject.
* Tailored to the needs of students of optimization and decision theory
* Written in a lucid style with numerous examples and applications
* Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity
* Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics
* Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters
* Contains exercises at the end of each chapter, with hints in an appendix
Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research. ... Read more

Book Description

This book is written is such a way that the level of mathematical sophistication builds up from chapter to chapter. It has been reorganized into four parts: basic analysis, analysis of feedback systems, advanced analysis, and nonlinear feedback control.Updated content includes subjects which have proven useful in nonlinear control design in recent years—new in the 3rd edition are: expanded treatment of passivity and passivity-based control; integral control, high-gain feedback, recursive methods, optimal stabilizing control, control Lyapunov functions, and observers.For use as a self-study or reference guide by engineers and applied mathematicians. ... Read more

Reviews (5)

An excellent textbook
This is an excellent textbook, outdoing, AS SUCH, the books by Vidyasagar, Isidori, and Rugh, as well as both of Minorsky's related classics. It is well written, well balanced, making extensive use of a fairly sophisticated language (not too abstract but certainly far from archaic), and features a plethora of exercises of various difficulty levels. Appendix A, presenting detailed, careful proofs of 21 theorems and lemmas is a definite "must." This appendix alone is worth the (sour) price of the book, making it today's "text of choice" when it comes to teaching courses. (Students should be familiar with ALL of them!)

The topics dealt with, while, for the most part, pretty standard, are appropriate for a first graduate course on nonlinear systems, as approached from the Control Engineering viewpoint. There's a bit of just about everything that's important in present-day studies of such systems: mathematical foundations, stability analysis, periodic solutions, averaging & pertubations (both regular and singular), feedback control & linearization, and Lyapunov-based design, including adaptive control. Even H-infinity is touched in passing!

Unfortuantely, the famous conjectures by Aizerman and Kalman and Letov's contributions do not constitute a central interest in the book. Lur'e's problem, on the other hand, IS mentioned.

The author provides a 195-title reference list and an effort to include recent texts is apparent. However, a few serious omissions do occur. For instance, Russian publications are nearly non-existing on said list, and Desoer's famous 1969 paper on the stability of slowly-varying systems is not mentioned explicitly. But it is not entirely accurate to say that Khalil's treatment of time-varying systems is centered around time-freezing techniques. He does, indeed, present one or two examples to that effect. But out of 734 pages, no less than 16 are dedicated to several aspects relating to stability of time-varying systems, most of which can be directly mapped back to Desoer's theorem.

By and large, this book is -- and shall remain for some time to come -- the best text for introductory graduate courses in Nonlinear Systems.

One of the very best texts currently on the market
Hassan Khalil's book (already in its second edition) has become a best-seller. Easy to understand why.

At the same time, the text manages to be very readable and fairly sophisticated. In fact, it is not very usual for Engineering texts to display such an advanced level of mathematical rigor. As a result, however, it is not entirely true that the book can be easily followed by undergrads. A reasonable degree of familiarity with -- or, rather, dexterity in -- the basics of Mathematical Analysis (with some topological underpinnings) is required. But, since the book is filled with theorems and rigorous proofs galore, grad students and research engineers with a strong penchant for Math are bound to welcome it as a bona fide blessing!

Unfortunately, it must be said that the book fails to make the 5-star rating for two reasons. First off, it is perhaps a bit too Electrical-Engineering-geared, nearly ignoring examples from other fields. Secondly, its treatment of time-varying systems is rather scanty, at best, basically relying on what can be ultimately traced to the intelectually dissatisfying time-freezing approach. (This is probably justifiable, since it would otherwise imply an additional 40-50 pages to make room for operator theory and Hilbert spaces, as is done, e.g., in the book by Feintuch & Saeks.)

Nevertheless, Prof. Hassan's is by far one of the best texts currently on the market.

Recommended
This book is excellent both as a textbook and as a referencemonography (it is in fact widely referenced in the literature). It isvery readable (at the level of Hirsch & Smale's classic "Differential equations, dynamical systems, and linear algebra"), and definitely accessible to undergraduates with some previous knowledge of ODEs. The first two chapters cover the basics (existence/uniqueness/continuation of solutions, motivating examples). Lyapunov's theorems and their applications are the core of the book, and are very carefully explained. The author covers autonomous/nonautonomous systems and the related invariance theorems; converse Lyapunov theorems, perturbed systems, input-output stability (very welcome here); stability of periodic orbits; perturbation theory. Many theoretical results are illuminated by examples. Researchers with an interest in robust control and stability of dynamical systems will find this book useful. The only reason for giving 4 stars to this book is its price. END

A necessary learning tool for Graduate Control engineers
Being a Ph.D. canidate in Control Theory at Georgia Tech, I am familiar with the essential tools needed to be sucessful in advanced control engineering. This book covers the entire spectrum of topics in control theory presented at many universities around the country. It is presented with a strong mathematical foundation and has many illustrative examples. Subjects covered include the fundamental properties of differential equations, basic and advanced stability theory, feedback control and the feedback linearization/computed torque method which is a very popular approach to nonlinear design. It also contains introductions to newer techniques such as adaptive and sliding mode control. In my studies at GT, i have more than once been plesently suprised to find tools in this book that i didnt expect to find there. For example, chapters 5-9 cover the improtant results that i was exposed to in a 3 course graduate level sequence in ODE's from the math department!!

This book is sugessted for any serious student of control theory and it is recommended that the reader be exposed to at least one introductory real analysis course.

A very well-written graduate level nonlinear systems book
This book is the most easy to understand, yet rigorously written nonlinear systems book on the market. It is very suitable for those interested in nonlinear controls. This book is also good as a reference book on nonlinear systems topics. The level of mathematical complexity matches the level of Ph.D. students, although it is sometimes difficult to follow. ... Read more

Reviews (1)

john wiley the publisher
John Wiley should be ashamed of your self This unbelivable price for a miserable paperbak print ... Read more

Book Description

This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be suitable for a course in functional analysis. The book also includes applications to partial differential equations, the stability and stabilization of linear systems, power signal spaces, and delay systems, treated from an input/output point of view. ... Read more

Book Description

"This book should appeal to readers with interests across the full spectrum from nonsmooth analysis to optimization, because it provides a clear illustration of some of the connections between these fields. The authors have done their part to nurture this important relationship..." -SIAM Review

This timely book in the area of optimization focuses on the questions of how solutions behave under perturbation, optimality conditions, and related issues. The authors have put together many results that are not easily accessible in the current literature organizing the material in a consistent manner so that a broad theory emerges. Many elements are new and not available elsewhere. ... Read more

Book Description

This book is designed for a first course in nonlinear optimization. It starts with classical optimization notions from calculus and proceeds smoothly to a study of convex functions. This is followed by material on basic numerical methods, least squares, Karush-Kuhn-Tucker theory, penalty functions, and Lagrange multipliers. The book has been tested in the classroom; the approach is rigorous at all times and geometric intuition is developed. The numerical methods are up-to-date. The presentation emphasizes the mathematical ideas behind computer codes. The book is aimed at the student who has a working knowledge of linear algebra and partial differentiation but has had no previous exposure to optimization. Mathematics instructors will be comfortable with the mathematical approach which deemphasizes recipes and emphasizes understanding underlying concepts. There are many exercises chosen to highlight the fundamental ideas. ... Read more

Reviews (2)

Peressini and Sullivan are not enough to make you Uhl
This book takes an unusual path to the usual results in optimization. Though refreshing in some ways, the standard results--Kuhn-Tucker conditions for non-convex programs--are not achieved until the last chapter. Little of the preceeding six chapters can be skipped without ruining this development! D.M. Greig, by comparison, develops this result in her first chapter, in a book at a comparable level. With Peressini et al, you sink weeks into learning restricted convex programs; an interesting niche, but one best studied once the main results are in hand.

Excellent first book on nonlinear programming.
I am a graduate student, working on a PhD in Optimization (nonlinear programming). This book provides an excellent first exposure to the field of nonlinear programming. It is full of "easily visualizable" 2 or 3 dimensional examples, which greatly aid in the development of strong intuition. Although the intended level of this book is the advanced undergraduate level, it serves as a very thorough and useful companion to any graduate text. This book almost single-handedly helped me pass my qualifying exam in optimization, mostly because it "made all of the pieces fit together."

I heartily recommend it to _anyone_ interested in learning about nonlinear programming. ... Read more

Book Description

This book concerns existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. The author obtains these necessary conditions from Kuhn-Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Fattorini studies evolution partial differential equations using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory.The author establishes existence of optimal controls for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls. ... Read more

Book Description

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. Its 11 chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Book Description

A thorough and highly accessible resource for analysts in a broad range of social sciences.

Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods.

Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include:

• More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics
• Classic results mixed with modern numerical methods to aid users of computer programs
• Extensive appendices containing mathematical details important for a thorough understanding of the topic

With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science,geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences. ... Read more

Reviews (1)

Good Reference for Optimization
This book carefully describs the fundamental and application of optimization. You can easily find the useful approach when you try to optimize your problem and know how to use it with the help of step-by-step illustration of that approach. ... Read more