Convex Analysis and Optimization

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9781886529458: Convex Analysis and Optimization

A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. Among its special features, the book: 1) Develops rigorously and comprehensively the theory of convex sets and functions 2) Provides a geometric, highly visual treatment of convex and nonconvex optimization problems, including existence of solutions, optimality conditions, Lagrange multipliers, and duality 3) Includes an insightful and comprehensive presentation of minimax theory and zero sum games, and its connection with duality 4) Describes dual optimization, the associated computational methods, including the novel incremental subgradient methods, and applications in linear, quadratic, and integer programming 5) Contains many examples, illustrations, and exercises with complete solutions (about 200 pages) posted on the internet.

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About the Author:

The principal author, Dimitri P. Bertsekas, is McAfee Professor of Engineering at the Massachusetts Institute of Technology (MIT) and a member of the prestigious National Academy of Engineering. The supporting authors, Angelia Nedic and Asuman E. Ozdaglar, hold PhDs from MIT, and are Professors at the Univ. of Illinois, and MIT, respectively.

Review:

The text is therefore ideally suited for classroom use. The prerequisite material, basic linear algebra and real analysis, is presented in the first chapter and is covered in undergraduate classes. The presentation stresses geometry and simple proofs at all times. --Serge G. Kruk, Mathematical Reviews, 2006

The book's treatment of convexity theory is rigorous, insightful, and quite comprehensive, with all major aspects of the subject receiving substantial treatment. The mathematical development is ambitiously novel and uses a handful of unifying principles that can be easily visualized and understood ... The writing style is very clear with many figures and exercises supporting the text ... This is a ground-breaking and highly pedagogical book on a fundamental subject, which will be greatly appreciated by students and researchers. I highly recommend this book. --P. Pardalos, Optimization Methods and Software

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