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A First Course in Optimization Theory
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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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Product details
Paperback: 376 pages
Publisher: Cambridge University Press; 1st US Edition 1st Printing edition (June 13, 1996)
Language: English
ISBN-10: 0521497701
ISBN-13: 978-0521497701
Product Dimensions:
6.9 x 0.8 x 10 inches
Shipping Weight: 1.4 pounds (View shipping rates and policies)
Average Customer Review:
4.1 out of 5 stars
23 customer reviews
Amazon Best Sellers Rank:
#315,727 in Books (See Top 100 in Books)
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.Finally, as far as I can tell, this book is missing any discussion of the Bolzano Weierstrass Theorem, which is an important result in economics.Update: The definition of a determinant is wrong in this book. It states you should take the negative of even permutations when it should be of odd permutations.
As described, thanks
A lot of the material here is subsumed in other texts. It also goes into more detail than you need for 1st year PhD courses.
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. Lagrangeans and Kuhn-Tucker optimization are the bread and butter of microeconomics, and yet few professors will bother to go into them in detail. This book succeeds in making these abstract mathematical procedures feel tangible and intuitive, defining them rigorously, explaining their usefulness and providing examples. This is one of very few books that I keep on my shelf for reference.For a broader (and equally necessary) introduction to the math that you'll need for advanced study in economics, I recommend Simon and Blume's Mathematics for Economists.
One of the probes that I have found with Kindle format is the size of the equations. The equations are to small to be readable. The equations size does not increase in size as text size increases.
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. However, there're a considerable amount of typos in it. For instance, the statement of the Lagrange's Theorem takes the function g(i) to R(k), which should be R(1), etc.. So be careful. Mine is 15th printing version, but no revisions so far.. I think the press has earned enough from the book and should consider a second edition, right? haha..
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?along with wrong definition for implicit function theorem in chapter 1 - missing minus sign in front.and look at page where they talk about epigraph and subgraph. and ... you get the point.i can't believe it has such basic definitions wrong.not to mention uncommon notations used for some analysis...not happy with the book.for optimization stick with Stephen Boyd, Bertsekas, or Luenberger.and for applying optimization tech to economics get simon, and blume2 stars might not seem a big deal to you but look at my rating history.i rarely go under 4 stars.stay away from this book. although if the author fixes those deluge of stupid mathematical mistakes this book has a potential to be 5 stars.
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 engage interesting problems.
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