A First Course in Optimization Theory

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.

Best graduate-level optimization textbook to start getting familiar with optimization and its applications in economics and business!

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..

Very insightful and direct-to-the-point book. If you need to master optimization topics in a short period of time, buy it. Its cookbook format also helps to organize the necessary steps of optimization theory in your mind.

Book is in perfect condition and without notes

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.

As described, thanks

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.