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.
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.
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.