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A First Course in Optimization Theory [Paperback]

Rangarajan K. Sundaram
4.3 out of 5 stars  See all reviews (16 customer reviews)

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Book Description

April 3, 2014 0521497701 978-0521497701
This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. 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. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

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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.

Product Details

  • Paperback: 376 pages
  • Publisher: Cambridge University Press (April 3, 2014)
  • Language: English
  • ISBN-10: 0521497701
  • ISBN-13: 978-0521497701
  • Product Dimensions: 9.9 x 7 x 0.7 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #89,133 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
34 of 36 people found the following review helpful
4.0 out of 5 stars Good introduction to the field of optimization 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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28 of 31 people found the following review helpful
5.0 out of 5 stars Great book and an even greater value December 7, 1999
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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40 of 50 people found the following review helpful
3.0 out of 5 stars Unless you're into theory, this book is NOT for you September 30, 2000
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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10 of 11 people found the following review helpful
5.0 out of 5 stars The title says it all April 1, 2004
By A Customer
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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15 of 19 people found the following review helpful
5.0 out of 5 stars Excellent book for PhD students in Operations Management September 2, 1999
By A Customer
Format:Paperback
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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Most Recent Customer Reviews
5.0 out of 5 stars Extremely Useful
Very insightful and direct-to-the-point book. If you need to master optimization topics in a short period of time, buy it. Read more
Published 4 months ago by Gustavo S. Cortes
5.0 out of 5 stars A good first book for PhDs
I read almost all the comments here on amazon.com before reading the book. I am on Chapter 5 now, and hence in some position to comment. I think the book is excellently written. Read more
Published 16 months ago by Bilal A. Siddiqui
2.0 out of 5 stars Great for reference, if you love jargon
This book lists itself as a "first course in optimization theory", which would imply any student nearing the end of their undergraduate degree or beginning their master's program... Read more
Published 20 months ago by Kevin Smith
5.0 out of 5 stars Great Overview of Optimization Theory
If you are studying Economics or Applied Mathematics, especially in Operations and Information Management, this book is an great overview of what you should master in order to... Read more
Published on September 18, 2011 by Chris Brightman
2.0 out of 5 stars topics covered are great but loses 3 stars because of ...
glaring mistakes all over the book.
i've found at least 3 wrong definition of convexity in the book. some contradicing within a paragraph. wow do some proof reading? Read more
Published on October 2, 2010 by S. Lee
4.0 out of 5 stars A nice treatment for econ grad, but lots of typos.. so be careful
I am a student at Penn econ. The book fits the requirement of the department very well. It is a nice treatment of the topic, both on the theoretical and applied sides. Read more
Published on July 31, 2010 by W. YANHAO
5.0 out of 5 stars A must-have reference
If you're a graduate student in economics, or perhaps computer science, buy this book as soon as possible. It will make your life much, much easier. Read more
Published on March 11, 2009 by Trevor Burnham
5.0 out of 5 stars Very self contained
This is a very readable introduction to optimisation that should appeal to a wide audience, althouh it is mainly aimed at economics students. Read more
Published on April 9, 2008 by M. Henri De Feraudy
5.0 out of 5 stars Great Review of Optimization for Graduates
This book is a great review prior to starting graduate study in economics. Its accessible even if you've never studied optimization before, and covers many of the main optimization... Read more
Published on January 3, 2007 by M. Geruso
4.0 out of 5 stars a good book...
a good book with lots of preliminary math review, but exercises are not that well
Published on October 17, 2005 by Mehmet Cicek
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