Convex Analysis and Optimization - Hardcover

Bertsekas, Dimitri

Hardcover

ISBN 10: 1886529450 ISBN 13: 9781886529458

Publisher: Athena Scientific, 2003

Synopsis

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.

About this title

About the Author

The principal author, Dimitri Bertsekas is McAffee Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, and a member of the National Academy of Engineering. He has researched a broad variety of subjects from optimization theory, control theory, parallel and distributed computation, systems analysis, and data communication networks. He has written numerous papers in each of these areas, and he has authored or coauthored sixteen textbooks. Professor Bertsekas was awarded the INFORMS 1997 Prize for Research Excellence in the Interface Between Operations Research and Computer Science for his book "Neuro-Dynamic Programming" (co-authored with John Tsitsiklis), the 2001 ACC John R. Ragazzini Education Award, the 2009 INFORMS Expository Writing Award, the 2014 ACC Richard E. Bellman Control Heritage Award for "contributions to the foundations of deterministic and stochastic optimization-based methods in systems and control," the 2014 Khachiyan Prize for Life-Time Accomplishments in Optimization, and the 2015 George B. Dantzig Prize. In 2018, he was awarded jointly with John Tsitsiklis, the INFORMS John von Neumann Theory Prize, for the contributions of the research monographs "Parallel and Distributed Computation" and "Neuro-Dynamic Programming". In 2001, he was elected to the United States National Academy of Engineering for "pioneering contributions to fundamental research, practice and education of optimization/control theory"

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

Edition details

• Publisher: Athena Scientific
• Publication date: 2003
• ISBN 10: 1886529450
• ISBN 13: 9781886529458
• Binding: Hardcover
• Language: English
• Number of pages: 560