Book Description

A modern, up-to-date introduction to optimization theory and methods
This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization.
Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides:
* A review of the required mathematical background material
* A mathematical discussion at a level accessible to MBA and business students
* A treatment of both linear and nonlinear programming
* An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods
* A chapter on the use of descent algorithms for the training of feedforward neural networks
* Exercise problems after every chapter, many new to this edition
* MATLAB(r) exercises and examples
* Accompanying Instructor's Solutions Manual available on request
An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business. ... Read more

Reviews (3)

Not For Undergraduates
This book should not be used to teach an Introduction to Optimization at the undergraduate level. It is being done so at my school, and it is driving the undergraduate students crazy because they do not understand the book, the notation also is causing problems. If you are new to the subject area, and do not have an advanced math background(more than college) try looking elsewhere.

took the class, liked the book
Drs. Chong and Zak are Professors of Electrical Engineering at Purdue, and Dr. Chong was the instructor for the ECE grad level optimization class when I took it spring '97. The book alone is good, detailed and rigorous enough for a graduate course without sacrificing readability or in-chapter examples. However, without the MATLAB examples that were developed by the authors to accompany lectures and illustrate each optimization method covered, the material might be a little abstract or dry for self-teaching. An excellent introduction or reference nonetheless, those without a solid base in linear algebra should keep a reference text handy while reading.

All industrial engineering student should buy this book.
An Introduction to Optimization ... Read more

Book Description

This up-to-date reference offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems--providing an overview of recent advances in control and systems theory, numerical linear algebra, numerical optimization, scientific computations, and software engineering. ... Read more

Reviews (1)

Algorithms for Linear-quadratic Optimization
2.1.1 Newton's method 98
2.1.2 Stabilization methods 101
2.2 Computation of Real Schur Form and Invariant Subspaces 105
2.2.1 Basic definitions and properties 105
2.2.2 Preprocessing algorithms 114
2.2.3 The QR algorithm 118
2.2.4 Real Schur form computation and ordering 135
2.3 Solving Sylvester and Lyapunov Equations 143
2.3.1 Solving Sylvester equations 144
2.3.2 Solving Lyapunov equations 159
2.3.3 Solving stable non-negative definite Lyapunov equations 162
2.4 Stabilization Algorithms 174
2.4.1 Full stabilization algorithms 174
2.4.2 Partial stabilization algorithms 177
2.5 Newton-Based Riccati Solvers 179
2.5.1 Algorithmic templates 180
2.5.2 Computational issues 183
2 5.3 Applicability and limitations 186
References 191
3 Schur and Generalized Schur Algorithms 197 ... Read more

Book Description

In the past three decades, local search has grown from a simple heuristic idea into a mature field of research in combinatorial optimization that is attracting ever-increasing attention. Local search is still the method of choice for NP-hard problems as it provides a robust approach for obtaining high-quality solutions to problems of a realistic size in reasonable time. Local Search in Combinatorial Optimization covers local search and its variants from both a theoretical and practical point of view, each topic discussed by a leading authority. This book is an important reference and invaluable source of inspiration for students and researchers in discrete mathematics, computer science, operations research, industrial engineering, and management science.

In addition to the editors, the contributors are Mihalis Yannakakis, Craig A. Tovey, Jan H. M. Korst, Peter J. M. van Laarhoven, Alain Hertz, Eric Taillard, Dominique de Werra, Heinz Muhlenbein, Carsten Peterson, Bo Soderberg, David S. Johnson, Lyle A. McGeoch, Michel Gendreau, Gilbert Laporte, Jean-Yves Potvin, Gerard A. P. Kindervater, Martin W. P. Savelsbergh, Edward J. Anderson, Celia A. Glass, Chris N. Potts, C. L. Liu, Peichen Pan, Iiro Honkala, and Patric R. J. Östergård. ... Read more

Book Description

This book provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences. ... Read more

Book Description

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

Reviews (3)

A classic and a bargain at that
I lost my original copy during my last move. Therefore, I was overjoyed that an inexpensive paperback version had been printed. A must for the numerical analyst's library.

good intermediate text on numerical analysis
This is a good intermediate text on numerical analysis. The development of the underlying real variable theory is much more rigorous than the closely related and more recent text "Numerical Recipes in C". Also, there is more attention paid to function theoretic considerations such as notions of continuity and compactness. This is basically an introductory numerical functional analysis textbook. There are numerous good examples sprinkled throughout the text. To get the most out of this book, you need a working knowledge of advanced calculus, real analysis and linear algebra.

Simply the best you can get (at this price)
This is the republication of the 2nd edition published by McGraw-Hill, 1978, with minor corrections. This Dover edition also includes 50 pages of Hints and Answers to Problems, which is very helpful. It is one of the 14 reference books listed in the Numerical Recipe in C: The Art of Scientific Computing, and the authors of the Recipe book says, of the 14 books, "These are the books that we like to have within easy reach." A. Ralston, of SUNY Buffalo, also co-wrote a book, Discrete Algorithmic Mathematics(DAM), which is easy and fun to read. But I am puzzled by the words - "Well-known and highly regarded even by those who have never used it." - on the back cover of the A K Peters edition of DAM. What do they mean? ... Read more

Book Description

¿The book is very well structured, very clearly written, very well motivated, and complete in its treatment of modeling, analysis and simulation. It will be a basic reference for whoever wants to deeply understand homogenization from the point of view of its application to optimal design. The treatment is right to the point, a quality that is very much appreciated by readers. In summary, I believe this text may become a main source for the subject of optimal design and shape optimization.¿¿Mathematical Reviews ... Read more

Reviews (1)

shape optimization by the homogenization method
i want to abstract the all chapter of this book ... Read more

Book Description

Numerical Optimization has numerous applications in engineering sciences, operations research, economics, finance, etc. Starting with illustrations of this ubiquitous character, this book is essentially devoted to numerical algorithms for optimization, which are exposed in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. The theoretical bases of the subject, such as optimality conditions, Lagrange multipliers or duality, although recalled, are assumed known. Most of the algorithms described in the book are explained in a detailed manner, allowing straightforward implementation. This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate, why they converge, difficulties that may be encountered and their possible remedies. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. ... Read more

Book Description

The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The first chapters introduce some worked examples of stochastic programming and demonstrate how a stochastic model is formally built. Subsequent chapters develop the properties of stochastic programs and the basic solution techniques used to solve them. Three chapters cover approximation and sampling techniques and the final chapter presents a case study in depth. A wide range of students from operations research, industrial engineering, and related disciplines will find this a well-paced and wide-ranging introduction to this subject. ... Read more

Reviews (2)

Formalism doesn't equal good introduction.
Given that there are not many books in the area of stochastic programming Birge et al have written a book that will be a necessary reference for the time being. The first third of the book does provide a good introduction to the basics of SP but after that a level of formalism dominates that makes one wonder if she is reading from an arcane optimization journal. The later two thirds of the book is really nothing more than an amalgam of results pulled from the literature (journals). As such, little motivation is provided for the major results that are for the most part just juxtaposed on after another. One wonders why such a journalistic style would be used for an introductory text. After all the subject should not be presented as a springer-verlag MATH text in a field like algebraic topology where a theorem-proof format is legimate. Thus, until a better introductory text comes along that blends more of the practical engineering aspects with the theory we must be content with the current state of the art.

A must own guide to Stochastic Programming
Introduction to Stochastic Programming is a must own book for anyone working in OR, IE, MS, etc. As stochasticity becomes more and more important in the field, this book becomes increasingly valuable. "Introduction" is a bit of a stretch. It starts from ground zero of Stochastic Programming, but is very heavy on the math. If you aren't solid with your LP and probability, then a brush up is definately in order. This book is not for the faint of heart. Nevertheless, Birge and Louveaux do an OUTSTANDING job. The examples are clear, easy to follow (assuming you're not math phobic) and very relevant. They go through different formulations of stochastic programms (recourse, chance constrained, etc.). The book discusses formulation, algorithms, and applications. There are not many books out there on Stochastic Programming...and this is really the only one you need to own. ... Read more

Book Description

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

Book Description

For over a decade, there has been an increasing interest in the use of supply chain methods to improve performance across the entire business enterprise. Numerous industries have recognized the importance of efficient supply chain integration, and, as a result, supply chain management has become a standard part of business practice.

Simultaneously, research interest in supply chain management has been growing at an increasing rate. Along with the implementation of supply chain management in practice, we have witnessed an explosive growth of research. These new research developments have found their way into practice, resulting in experiments using these developments. This implementation and experimentation has naturally lead to new ideas, hence the practice-research-practice-research cycle continues.

The Practice of Supply Chain Management: Where Theory and Application Converge is a must-have volume for users of supply chain management methods, supply chain management researchers, and students in supply chain management. The objective of The Practice of Supply Chain Management: Where Theory and Application Converge is to provide an overview of this important practice-research cycle. The focus of the book is on supply chain practice, but supply chain practice that has been heavily influenced by supply chain research. It is this synergy between research and practice that continues to stimulate new directions for research.

The Practice of Supply Chain Management: Where Theory and Application Converge is organized into three sections: Core Concepts and Practices; Emerging Supply Chain Practices; and Supply Chain in Action. The Practice of Supply Chain Management: Where Theory and Application Converge will provide the reader:

A set of tutorials on key supply chain methods and practices;
A review of supply chain practices in multiple industries;
A description of how innovative ideas and new research methodologies have been used in practice;
An identification of the enablers of successful implementation of such ideas in practice;
A report on the new insights and research directions that can be gained from observing these practices. ... Read more

Book Description

This book is intended for a one year graduate course on Lie groups.    Rather than providing a comprehensive treatment, the author emphasizes the beautiful representation theory of compact groups.  However, this book also discusses important topics such as the Bruhat decomposition and the theory of symmetric spaces. ... Read more

Book Description

Vol. 1 of Lars Hörmander's influential 4-volume treatise is a detailed exposition of the theory of distributions. From the reviews: 'In order to illustrate the richness of the book: in my review of the 1983 edition [...] I gave a list of 20 subjects which were new compared to Hörmander's book of 1963. Most of these subjects concern important, basic and highly nontrivial theorems in analysis. Hörmander's treatment of these is extremely clear and efficient and often highly original. [...] Most of the exercises are witty, with an interesting point. The phrasing of both the exercises and the answers and hints is very careful [...] In all, the book can be highly recommended, both as a textbook for advanced students, and as background and reference for introductory courses on distributions and Fourier analysis. J.J. Duistermaat in Mededelingen van het Wiskundig Genootschap. ... Read more

Reviews (1)

the definitive guide to micro-local analysis
Hormander's four volume guide to linear partial differential operators is the definitive guide to smooth micro-local analysis from the man who invented a large fraction of it.

Micro-local analysis is an approach to the analysis of singularities of variable coefficient linear partial differential equations based on the use of the Fourier transform and of symplectic geometry. Ideas from Hamiltonian physics and quantum theory also feature heavily. The fact that the subject is a mixture of analysis and geometry makes it beautiful and powerful.

The four volume set is hard work and in some ways is more useful as a reference work than as a learning book but on the other hand, all the material is there and the books do reward the reader who is willing to spend the time to study them carefully.

The first volume is the most accessible and the second paperback edition carries the added benefit of included exercises with partial answers which are often highly informative. ... Read more

Book Description

Book Description

Linear Statistical Models

Developed and refined over a period of twenty years, the material in this book offers an especially lucid presentation of linear statistical models. These models lead to what is usually called "multiple regression" or "analysis of variance" methodology, which, in turn, opens up a wide range of applications to the physical, biological, and social sciences, as well as to business, agriculture, and engineering. Unlike similar books on this topic, Linear Statistical Models emphasizes the geometry of vector spaces because of the intuitive insights this approach brings to an understanding of the theory. While the focus is on theory, examples of applications, using the SAS and S-Plus packages, are included. Prerequisites include some familiarity with linear algebra, and probability and statistics at the postcalculus level.

Major topics covered include:

• Methods of study of random vectors, including the multivariate normal, chi-square, t and F distributions, central and noncentral
• The linear model and the basic theory of regression analysis and the analysis of variance
• Multiple regression methods, including transformations, analysis of residuals, and asymptotic theory for regression analysis. Separate sections are devoted to robust methods and to the bootstrap.
• Simultaneous confidence intervals: Bonferroni, Scheffé, Tukey, and Bechhofer
• Analysis of variance, with two- and three-way analysis of variance
• Random component models, nested designs, and balanced incomplete block designs
• Analysis of frequency data through log-linear models, with emphasis on vector space viewpoint. This chapter alone is sufficient for a course on the analysis of frequency data.

Reviews (4)

The way linear models should be taught
Approach of linear models from a geometric point of view is often addressed in a single lecture or chapter and does not provide much assistance in the understanding of the material. This book, however, presents all material usually covered in a linear models book from this approach. For those who have learned models both ways, proofs and applications using these geometrical concepts are much less cumbersome than the standard matrix algebra manipulation. Additionally, having a solid understanding of this material is a greater help in the understanding of more advanced topics. As stated, the book is dense and previous exposure is useful if the reader is not assisted by a knowledgeable instructor.

Elegant and practical treatment
I've used this text twice for a one-semester graduate course in linear models, emphasizing Chapters 1,2,3,5,6, and would use it again. It is outstanding.

The best feature of the book is its consistent theme: a least squares estimator is an orthogonal projection onto a subspace, which can be evaluated by orthogonal decomposition of the subspace. This gives the subject the elegance of pure mathematics, while at the same time making complex topics such as two-way and three-way analysis of variance readily accessible.

The second-best feature of the book is the extensive collection of problems. Most are just at the right level, not simply cookbook plug-in type exercises, but problems that require understanding, yet not too difficult for the average student, who is typically not a math major. A few of the problems require statistical software, but most do not.

The only negative aspect of the book is the large number of errata, although this does have the advantage of teaching the students to adopt a healthy degree of skepticism.

Thanks
I thank Mr. Peng for saying the book "would serve as a decent linear models reference." J. Stapleton

Very compact book, not an introductory text
This book is very compact, which for me was one of its negative qualities. Part of the problem is the way the book is printed, with many proofs and mathematical statements embedded in the text rather than on lines by themselves. I imagine this saves in printing costs but it makes the text relatively unreadable. This book, however, would serve as a decent linear models reference . ... Read more