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A First Course in Optimization Theory 130.65 edition Edition

4.2 out of 5 stars 21 customer reviews
ISBN-13: 978-0521497701
ISBN-10: 0521497701
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Editorial Reviews

Review

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

Book Description

Divided into three separate parts, this book introduces students to optimization theory and its use in economics and allied disciplines. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.
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Product Details

  • Paperback: 376 pages
  • Publisher: Cambridge University Press; 130.65 edition edition (June 13, 1996)
  • Language: English
  • ISBN-10: 0521497701
  • ISBN-13: 978-0521497701
  • Product Dimensions: 6 x 0.8 x 9 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (21 customer reviews)
  • Amazon Best Sellers Rank: #186,977 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on March 20, 2001
Format: Paperback
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.Read more ›
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Format: Paperback
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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Format: Paperback
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.
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By A Customer on April 1, 2004
Format: Paperback
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.
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Format: Paperback Verified Purchase
This book mostly has clearly written proofs and easy-to-follow explanations for students who have some experience in proofs or basic analysis. In my opinion, it is definitely not a book for someone who has only seen calculus.

However, I have three very large problems with this book.

The first, and most important, is that the book is not self contained. In many theorems in Chapter 1, the reader is asked to see Baby Rudin for the proof. While it's pretty easy to find a PDF of Baby Rudin online for free, this is still not ideal. First, because Rudin and this book use different terminology/symbols for the same concepts, so there is a bit of unnecessary complexity in figuring how out Rudin's proof fits into this book's theorem. For example, the proof of Theorem 1.21 in this book is left to the proof of Rudin's Theorem 2.41. However, Rudin relies on the concept of k-cells, which this book never speaks of. Second, and most importantly, Rudin's proofs rely on concepts that this book has not defined. For example, Theorem 1.28 in this book relies on the proof of Theorem 2.36 in Baby Rudin. However, the proof in Baby Rudin relies on the concept of an "open cover," which this book does not define until a couple theorems later!

The second complaint I have about this book is that sometimes the proofs are sloppy. For example, at the beginning of section 1.2.8, the author states that unbounded sets must be compact and states that an unbounded sequence cannot contain a convergent subsequence. Instead of explaining why, though, he simply puts "(why?)" in the text. While this might be great for a student who is following this book in a class or with an instructor, this is incredibly frustrating for someone who is studying on their own.
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