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A First Course in Optimization Theory (Englisch) Taschenbuch – 29. August 1996

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'… the book is an excellent reference for self-studies, especially for students in business and economics.' H. Noltemeier, Würzberg

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This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first part examines the existence of solutions to optimization problems in Rn, 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.

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This chapter lays the mathematical foundation for the study of optimization that occupies the rest of this book. Lesen Sie die erste Seite
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Format: Taschenbuch
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.
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Format: Taschenbuch
An excellent book on optimization theory, I can recommend it without hesitation. The book starts out with introducing the problem of optimization in Euclidean spaces before delving into area which undergraduate students/high school students identify with optimization: Setting the first derivative to zero. In later chapters, the book covers constrained optimization (Langrange and Karush-Kuhn-Tucker), convex optimization, quasi-convex optimization (which is rarely covered in related books, as far as I know), parameterized optimization and dynamic programming.

One of the best chapters of this book are those on constrained optimization: The theorems of Langrange and Kuhn-Tucker are derived, together with a cook-book procedure on how to apply them, and thorough explanation why they often work and in which cases they don't. I really appreciated all results in the book being rigorously proved, not shying away from difficult mathematics -- the book contains a very generous chapter on mathematical preliminaries, making sure it is self-contained. The book also covers apparently totally unrelated topics, such as fixed-point theorems (Tarski, Brouwer) -- only to proof the existence of Nash equilibria as a corollary. Another great feature is the huge amount of short examples, illustrating why certain conditions are necessary for lemmas and theorems. Longer examples based on economics are re-used throughout the book, making an absolutely consistent picture.
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Format: Taschenbuch
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.
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Amazon.com: HASH(0x9f95b72c) von 5 Sternen 20 Rezensionen
35 von 38 Kunden fanden die folgende Rezension hilfreich
HASH(0x9f981714) von 5 Sternen Good introduction to the field of optimization 21. März 2001
Von Dr. Lee D. Carlson - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
28 von 32 Kunden fanden die folgende Rezension hilfreich
HASH(0x9f9874ec) von 5 Sternen Great book and an even greater value 8. Dezember 1999
Von Andrew Cusano - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
49 von 61 Kunden fanden die folgende Rezension hilfreich
HASH(0x9f983a98) von 5 Sternen Unless you're into theory, this book is NOT for you 30. September 2000
Von Ernest Blair - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
10 von 12 Kunden fanden die folgende Rezension hilfreich
HASH(0x9f9886c0) von 5 Sternen The title says it all 2. April 2004
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
15 von 20 Kunden fanden die folgende Rezension hilfreich
HASH(0x9f98842c) von 5 Sternen Excellent book for PhD students in Operations Management 2. September 1999
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
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