Convex Analysis and Optimization

by Dimitri P. Bertsekas
with Angelia Nedic and Asuman E. Ozdaglar

ISBN: 1-886529-45-0
Publication: April, 2003, 560 pages, hardcover
Price: $89.00

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A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization.

This major new book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Nonlinear Programming (Athena Scientific, 1999), Network Optimization (Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).

Aside from a thorough account of convex analysis and optimization, the book aims to restructure the theory of the subject, by introducing several novel unifying lines of analysis, including:


From the review by Panos Pardalos (Optimization Methods and Sofware, 2003):

"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. "

From the review by Serge G. Kruk (Mathematical Reviews, 2006):

"The text is therefore ideally suited for classroom use. The pre-requisite 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."

Among its features, the book:

Dimitri P. Bertsekas is McAfee Professor of Engineering at the Massachusetts Institute of Technology and a member of the prestigious United States National Academy of Engineering. He is the recipient of the 2001 A. R. Raggazini ACC education award and the 2009 INFORMS expository writing award. Angelia Nedic, is Assistant Professor, Univ. of Illinois. Asuman E. Ozdaglar, is Associate Professor, Massachusetts Institute of Technology.


Supplementary Material:

The material listed below can be freely downloaded, reproduced, and distributed.


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