Book Description

Data Envelopment Analysis (DEA) has grown into a powerful quantitative, analytical tool for measuring and evaluating performance. It has been successfully applied to a host of different entities engaged in a wide variety of activities in many contexts worldwide. DEA's "data-oriented" approach has been widely used in evaluating the efficiency and productivity of many different kinds of entities engaged in many different kinds of activities in many different contexts. DEA opens up possibilities for use in cases which have been resistant to other approaches because of the complex and often unknown nature of the relationships between their many activities. In addition, DEA is used to provide new insights into activities and entities that have previously been evaluated by other methods.

This Handbook has been developed as a comprehensive reference for researchers, students and practitioners. It reflects the state-of-the-art in Data Envelopment Analysis. It also represents a milestone in the progression of a continuously advancing methodology. which has extensive utility. Written by experts - who are the major research contributors to the topics covered - the Handbook is organized in three sections. The first section is a comprehensive examination of the basic DEA models and DEA extensions. The second section consists of a collection of coverages by persons experienced in applications to the areas of banking, education, sports, retailing, health care, etc. The final section is a review of current DEA software technology. ... Read more

Reviews (1)

THE BIBLE OF DEA
This wonderful gem of a book deals with all aspects of DEA. The collection of articles by leaders in DEA is second to none. Anyone interested in using efficiency as a performance tool will learn the ins and outs by reading this handbook. Hope there is a second volume. ... Read more

Book Description

Book Description

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.

This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading. ... Read more

Reviews (1)

Excellent introduction to Topology.
This is a good book for the first year in PhD studies. I recommend amply this book, it's very clear in the explanation, if you have any doubts about topology, Rockafellar explained in this book very simple the theory and all you need about Topology. ... Read more

Book Description

This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems.

The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference.

For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra. ... Read more

Reviews (1)

I understood it!
Looking for a text that explains the maths and the implementation of optimisation? I needed to write a program that included numerical optimisation, but I didn't understand the maths. I'd tried to read some other books on the subject, but I gave up because they presumed too much background knowledge and because they were written in an academic format (all proofs, greek letters and algebra) too obscure for me to wade through.

This book explains everything in plain english. When there is a new concept to be introduced, they begin with a practical example of the problem and then step through the solution. Any proofs are accompanied by graphs and words. The emphasis is on practicality and concepts rather than algebraic rigour.

I recommend this book to anyone who needs to create their own optimisations, or who wants to understand what goes on inside their software. ... Read more

Book Description

* Unique in its survey of the range of topics.
* Contains a strong, interdisciplinary format that will appeal to both students and researchers.
* Features exercises and web links to software and data sets. ... Read more

Reviews (1)

Recommended to scholars and graduate students
Introduction to Stochastic Search and Optimization provides comprehensive, current information on methods for real-world problem solving, including stochastic gradient and non-gradient techniques, as well as relatively recent innovations such as simulated annealing, genetic algorithms, and MCMC. It is written to be read and understood by graduate students, industrial practitioners, and experienced researchers in the field. Web links to software and data sets, and an extensive list of references of the book allows the reader to explore deeper into certain topic areas. I also found the index to be very comprehensive and carefully done. The appendices are as a refresher and summary of much of the prerequisite material. The book is somewhat unique in providing a balanced discussion of algorithms, including both their strengths and weaknesses. The book is among very few books that have integrated essential parts of statistical fields with optimization and decision making. The book's inclusion of a chapter on optimal experimental design is an example of such integration. The approaches discussed in the book could be used for financial decision making, forecasting, and quality improvement, among many other areas. ... Read more

Book Description

Empowering users with the knowledge necessary to begin using mathematical programming as a tool for managerial applications and beyond, this practical guide shows when a mathematical model can be useful in solving a problem, and instills an appreciation and understanding of the mathematics associated with the applied techniques. Surveys problem types, and discusses various ways to use specific mathematical tools. Contains prerequisite material for the study of linear programming, and offers a brief introduction to matrix algebra. Discusses the special structures of four network problems: the transportation problem, the critical path method, the shortest path problem, and minimal spanning trees. Covers compound interest and explores the financial aspects of specific problems considered throughout the book. Touches on "mathematics" oriented (vs. applications) material, with integrated proofs and discussions on such topics basic graph theory, linear algebra, analysis, properties of algorithms, and combinatorics. An extensive appendix section includes answers to many problems, an introduction to the linear programming package LINDO, an overview of the symbolic computation package Maple, and brief introductions to the TI-82 and TI-92 calculators and their applications. ... Read more

Book Description

Addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequality constraints. Provided are methods for modeling complex problems via effective algorithms on modern computers. The general theory and characteristics of optimization problems are presented, along with effective solution algorithms. Explores linear programming and network flows, employing polynomial-time algorithms and various specializations of the simplex method. Includes many numerical examples to illustrate theory and techniques. ... Read more

Reviews (8)

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

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

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

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

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

Best Math oriented LP book
I used this book as part of my grad level LP course that covered the first half of the book. Let me start out by saying that this is by no means a beginner's book. This book assumes a strong Linear Algebra and basic OR (assumes you know the Simplex method solution procedure, etc.) knowledge.If you are looking to get these OR prerequisites, then refer to the basic OR books by Hillier & Lieberman, Wayne Winston, Ignizio & Cavalier or A. Ravindran; this book is not for you.

This book is outstanding for understanding the theory and mathematical mechanics of LP and the first half of the book covers this comprehensively. The excercises in this book are outstanding (and can be hard). For those who need this book but are weak or rusty on the basics (like I was :) ) refer to one of the books above (I liked the Ignizio & Cavalier book a lot). I can't comment on the Network flows part of the book but it will almost surely be excellent if it is anything like the first half.

An excellent book for the intended audience.

THE Linear Programming Book.
I came across this book as a graduate student and hated it! But as I went deeper into Linear Programming (and stochastic programming) I realized the true worth of this book. It is definitely an intermediate-advanced level book rather than a beginner's book. Each concept is developed in painstaking detail with a strong base in Linear Algebra.
While the linear programming part is quite strong on the traditional algorithms, it is a little weak on interior point algorithms. For network flows, I would suggest the book by Ahuja et al... not because this book is bad but simply because Ahuja's done an unbeatable job.
Bottomline: This book is the best there is for a strong background in linear programming. If you are interested in theory look up Schrijver's "Theory of Linear and Integer Programming".

Amazing book
This is an amazing book for learning Linear programming but not very good for network flows. But the names given and symbols may vary from other books. I reccomend sticking to one LP book and following the conventions. I liked most of the conventions in this book except some. Some of the problems were dealt too complication liem dealing the lower bounds on variables. Good excercises at end of each chapter. I recommend this book strongly but I am afraid you would need guidance from a teacher if you want to learn Lp for the first time. I reccommend Ahuja's boof for Network flows. ... Read more

Book Description

The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory. ... Read more

Book Description

Modeling is a tool used by savvy business managers to understand the processes of their business and to estimate the impact of changes. Dynamic Modeling for Business Management applies dynamic modeling to business management, using accessible modeling techniques that are demonstrated starting with fundamental processes and advancing to more complex business models. Discussions of modeling emphasize its practical use for decision making and implementing change for measurable results. Readers will learn about both manufacturing and service-oriented business processes using hands-on lessons. Then will then be able to manipulate additional models to try out their knowledge and address issues specific to their own businesses and interests. All of the models used in the book and a run-time version of the ithink software are included on a CD-ROM included with the book. Some of the topics covered include workflow management, supply- chain management, and strategy. ... Read more

Reviews (1)

Good Book and Can Easily Be Put into Practice...
I read this after Sterman's 'Business Dynamics'. While 'Business Dynamics' is a graduate level text book, this book is more aligned to the requirements of practitioners like consultants and managers. MDS have a series of books on use of dynamic modeling, each focusing on a specific area like biological systems, economics, health sciences, environmental systems etc. ... Read more

Book Description

Brings the knowledge of 24 experts in this maturing field out from the narrow confines of academic circles, and makes it accessible to graduate students and power electronics professionals alike.
* Provides practicing engineers with the knowledge to predict power requirement behavior.
* The insights gained from this all-inclusive compilation will ultimately lead to better design methodologies. ... Read more

Reviews (2)

A Good Start Toward Automated Reasoning
This book is a good introductory catalog of automated reasoning concepts and methods. But I believe that programmers who are going to write automated reasoning systems should augment their computer knowledge (of logic) by learning a full- blown (serial, not tree) logical notation for both 1st and 2nd order predicate calculus.

Solving the inference problem is NP-Complete, and computational cycles explode as the number of premisses increase. Automated methods of solving the inference problem are often O(n^2) and often infeasible, for "real-world" problems. Most programmers don't have a broad enough horizon in formal logic to quickly recognize WHEN a certain automated technique will be useful.

I suggest a symbolic logic text such as Copi's Symbolic Logic, 5th ed., and then aggressively read about optimizing methods which are currently being developed (ex. Optimization Methods for Logical Inference, Chandru et alia).

However, as an introduction, the reviewed book is excellent.

Excellent Textbook for a First Logic Course in CS
I really liked this book. It is full of examples, and the explanations are clear and concise. The book guides you through predicate logic and first order logic and procedures for automated deductive systems for them. No previous knowledge is assumed. The book is also full of exercises and problems.

I do recommend this book for students of Computer Science and Mathematics who want to start learning about automated deductive systems and axiomatic theories. ... Read more

Book Description

Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization.

The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied:

+The two-phase simplex method; +The primal--dual simplex method; +The path-following interior-point method; +The homogeneous self-dual methods.In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows.Also, check the book's webpage for new online instructional tools and exercises that have been added in the new edition. ... Read more

Reviews (3)

Professor Robert Freund's review
This is a much more detailed one as compared to the other two and was penned by MIT ORC Professor Robert Freund.

Summary. This book presents a thoroughly modern treatment of linear programming that achieves a healthy balance between theory, implementation, computation, and between the simplex method and interior-point methods. It's most novel feature is that it is written in a delightful and refreshing conversational style, that bespeaks the author's teaching style and relaxed wit. It is a pleasure to read: students will find the book to be friendly and engaging, while professors will find in the book a wealth of teaching material, nicely organized and packaged for classroom use. The book is also meant to be used in conjunction with a public-available website that contains software for various algorithms, additional exercises, and demos of algorithms.
The need for new linear programming textbooks. The world of linear programming has changed dramatically in the last ten years. For one thing, the incredible changes in computer technology have made it easy to solve truly huge LPs, and routine LP problems solve in fractions of a second even on a personal computer. As a result, the study of linear programming algorithms is of less interest to the casual student. (In a similar vein, we usually do not teach students how to efficiently compute square roots; we simply presume they can press the right buttons on their calculator.) On the other hand, because we can now solve truly gigantic linear programs, issues of computer implementation, numerical stability, and software architecture, etc., are as important for the serious optimizer as is, say, duality theory. Furthermore, the development and recognition of the importance of interior point methods has changed the landscape of linear programming significantly, so that linear programming is no longer synonymous with the simplex method, and a modern treatment of LP must also present an in-depth treatment of the most important interior point methods.

Vanderbei's book is thoroughly modern. Vanderbei's book is completely up-to-date. Aside from a nice treatment of the simplex method, it also contains a very up-to-date treatment of interior point methods, including the homogeneous self-dual formulation and algorithm (which might soon become the dominant algorithm in practice and theory). It contains extensive material on issues of implementation of both the simplex algorithm and interior point algorithms. A politician might call it a book for the 21st century.

Vanderbei's book has many novel features. This book is quite different from most other textbooks on LP in a number of important ways. For starters, the standard form of a linear program in the book is the symmetric form of the problem (max c^T x | Ax <= b, x >= 0), as opposed to the usual form (min c^T x | Ax=b, x >= 0). This difference allows for an easier treatment of duality, and allows one to see the geometry of linear programming more easily as well. The symmetric form also makes it easier to set up the homogeneous self-dual interior point algorithm. However, this form has the drawback that discussions of bases, basic feasible solutions, and some of the mechanics of the simplex method are all a bit more awkward. (The book uses the language of dictionaries to describe the essential information in a simplex method iteration.) The book has more of a focus on engineering applications than does the more typcial LP textbook (which tend to rely on business problems). For example, there is a nice chapter on optimization of engineering structures such as trusses. The book gives a very broad treatment of interior point methods, including several topics that are not usually found in textbooks such as the homogeneous self-dual formulation and algorithm, quadratic programming via interior point methods, and general convex optimization via interior point methods.

These novel features are good in that the author has clearly tried to be innovative and to build an LP text from the ground up, without regard for past texts.

Some Nice Features. There are some particularly nice features in the book. The book contains a much-simplified variant of the Klee-Minty polytope that allows for a more straightforward proof that the simplex method can visit exponentially many extreme points. In addition to proving strong duality, the book also presents Tucker's strict complementarity theorem, which has become important in the new view of sensitivity analysis, optimal partitions, and interior point methods. The book also contains a nice treatment of the steepest edge pivot rule, which has recently emerged as an important component in speeding up the performance of the simplex algorithm. In the treatment of interior point methods, the author spends very little time on polynomial time bounds and guarantees (as a theorist, I like to see this material), instead adding value by discussing important computational and implemention issues, including ordering heuristics, strategies for solving the KKT system by Newton's method, etc. The book sometimes has an engineer's feel for the proofs, which is good for students but is a bit frustrating to hard-core math types such as myself. There are many instances where the proof is just a proof via an example. This is consistent with the conversational and informal style of the text, and this informality spills over into the mathematics on occasion.

This book has style. As mentioned earlier, the book has a wonderfully appealing conversational style. While the author does not purposely go out of his way to be cute and corny, he succeeds in leaving the reader grinning with his humor. There are some passages that are downright funny, but the style succeeds mostly by default. One section on the issue of modeling the anchoring of truss design problems is called Anchors Away, the subsection on updating factorizations to reduce fill-in is aptly called Shrinking the Bump. And there is the hint of a racy discussion of an application of Konig's Theorem involving boys and girls that the curious reader might enjoy.

Overall, I greatly enjoyed reviewing this book, and I highly recommend the book as a textbook for an advanced undergraduate or master's level course in linear programming, particularly for courses in an engineering environment. In addition, the book also is a good reference book for interior point methods as well as for implementation and computational aspects of linear programming. This is an excellent new book.

Excellent book
Very clearly written. Unlike most math books, the notation is easy to understand for engineers and programmers. I found the free online version first, and then decided to buy the hard copy.

Profesor
That book is excelent from class and practice. Very important in undergraduate and postgraduate. Thanks you. ... Read more

Book Description

Generalized linear models provide a unified theoretical and conceptual framework for many of the most commonly used statistical methods. In the ten years since publication of the first edition of this bestselling text, great strides have been made in the development of new methods and in software for generalized linear models and other closely related models.Thoroughly revised and updated, An Introduction to Generalized Linear Models, Second Edition continues to initiate intermediate students of statistics, and the many other disciplines that use statistics, in the practical use of these models and methods. The new edition incorporates many of the important developments of the last decade, including survival analysis, nominal and ordinal logistic regression, generalized estimating equations, and multi-level models. It also includes modern methods for checking model adequacy and examples from an even wider range of application. Statistics can appear to the uninitiated as a collection of unrelated tools. An Introduction to Generalized Linear Models, Second Edition illustrates how these apparently disparate methods are examples or special cases of a conceptually simple structure based on the exponential family of distribution, maximum likelihood estimation, and the principles of statistical modelling. ... Read more

Reviews (4)

the most clearly written book on the topic
My copy of the second edition just arrived yesterday and it is even better than the first edition (which was fantastic). The logical organization and clarity of writing make this book a 'must have' for any statistician's library. I'd give it 6 stars if I could. Readers should also check out McCulloch and Searle's 'Generalized, Linear and Mixed Models'.

Excellent concept - Execution could be better
I wish somebody would write a concise tutorial of the matematics required for an "intermediate" book such as Dobson's. Undoubtedly for someone whose acquaintence with modern statitical methods is more current this book is a gem. For someone like myself who wants a refresher and whose math is a bit rusty it leaves something to be desired. Some of the theoretical derivations in chapters 3 and 4 (keys to the understanding of the rest of the book) would be improved by a bit more detail and a thoroughly worked example. A major shortcoming is the lack of answers to the excercises; I don't see how the book was published without them. If the book was 100 pages longer with the addition of the aforementioned material, I would have given it a five star rating.

recommended for applications and clarity
...

Bill recommended Dobson's text because of her clear writing style and many useful examples. Dobson also places the theory in the context of the general exponential family of distributions. As I knew that the second edition was about to come out I waited for it.

The wait seems to have been very worthwhile. The second edition is a real bargin.... She has updated it with the many advances that have occurred over the past 12 years since the first edition was printed. This edition now includes some discussion of generalized additive models, broader coverage of applications as survival analysis, GEE, multi-level models and nominal and ordinal logistic regression have been added. It now offers the reader more applications in a wider variety of disciplines and includes modern approaches to diagnostic checking of the models.

As with the first edition, exploratory techniques are emphasized particularly graphical methods. The goal is to unify the apparently disparate statistical techniques that students are exposed to, into one general modeling framework.

It includes a nice up-to-date bibliography and recent advanced results on longitudinal models. The level is intermediate statistics with introductory statistics and linear models taken to be prerequisites. Students are also required to have some familiarity with calculus and linear algebra.

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This book provides a surprisingly brief and gentle, yet thorough, introduction to the subject of modeling dependent variables that are not continuous (see note below). The reader, who should be familiar with calculus-based probability, may initially find it frustrating that the actual practice of modeling nominal data is not discussed until the last two chapters (of 9). However, the cause for delaying the discussion of these models is to introduce the terminology and methodology of generalized linear models through more familiar linear regression models.

Thus, while this book is not ideal for someone who wants to jump right into the thick of building logistic, loglinear, or other models for nominal data, it is quite suitable for those wishing a thorough introduction to the practice of generalized linear modeling. For greater detail, a thicker book like McCullagh & Nelder's _Generalized Linear Models_ would be suitable.

Note: While the term "Generalized Linear Models" includes linear regression models (i.e., models for continuous dependent variables), reading this book is not the easiest way to be introduced to regression. A better starting point would be Draper & Smith's _Applied Regression Analysis_ or Weisberg's _Applied Linear Regression_. ... Read more

Book Description

The goal of the book is threefold; first, to serve as a reference for the enormous amount of existing clustering concepts and methods; second, to be used as a textbook; and, third, to present the author's and his Russian colleagues' results in the perspective of current developments. It contains several unique features: - It is the only book to contain an up-to-date review of clustering including the most recent theories about discrete clustering structures (subsets, partitions, hierarchies etc.) in their relation to data.- An approximation framework is developed as a major construct substantiating and extending such existing approaches as agglomerative clustering and K-means method, and leading to new methods such as box and ideal type clustering, uniform partitioning, aggregation of flow tables, and principal cluster analysis:- The opening chapter is devoted to a review of classification and clustering goals and forms prior to defining the scope and goals of clustering.- A dozen real-world illustrative examples are interwoven throughout the exposition. Audience: The book will be useful to both specialists and students in the field of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines. ... Read more

Book Description

Designed for a course in linear programming at the undergraduate and graduate levels for students of engineering and mathematics, this classic work provides a thorough, theoretical introduction to linear programming. Coverage of applications and nonlinear programming is included. ... Read more

Book Description

Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input--output analysis, portfolio investment, information analysis, and linear and nonlinear programming.While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader. ... Read more

Book Description

The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. ... Read more

Book Description

This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised. ... Read more

Reviews (1)

Required background reading...
..if you want to understand the much of Arnol'd's book on classical mechanics. Written for physicists in language that physicists can follow, the book starts with advanced calculus (geometry of surfaces and curves in 2D and 3D) and provides a readable and informative introduction to Riemannian geometry, including connections defined by structure coefficients of a Lie algebra, all the way through gauge theories. However, the books by Schutz and by Nakahara cover interesting topics not included here, so see them as well. ... Read more