Convex Optimization Theory Author:Dimitri P. Bertsekas An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. — Convexity theory is developed in a simple accessible manner, using easily visualized proofs. The book is supplemented by a long web-based chap... more »ter (over 160 pages), which covers the most popular convex optimization algorithms (and some new ones), and can be downloaded from the Athena Scientific website
Among its features, the book:
* develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar
* provides a geometric, highly visual treatment of convex optimization problems
* includes an insightful and comprehensive presentation of minimax theory and zero sum games
* contains many examples and illustrations in the text, and exercises with complete solutions posted on the internet
* connects with a supplementary freely downloadable, periodically updated chapter on convex optimization algorithms
* is structured to be used conveniently either as a standalone text for a theoretically-oriented class, or as a theoretical supplement to an applications/models class.
From the review by Panos Pardalos (Optimization Methods and Sofware, 2010): "The textbook, Convex Optimization Theory (Athena) by Dimitri Bertsekas, provides a concise,
well-organized, and rigorous development of convex analysis and convex optimization theory.
Several texts have appeared recently on these subjects ... The text by
Bertsekas is by far the most geometrically oriented of these books. It relies on visualization to
explain complex concepts at an intuitive level and to guide mathematical proofs. Nearly, all the
analysis in the book is geometrically motivated, and the emphasis is on rigorous, polished, and
economical arguments, which tend to reinforce the geometric intuition."« less