Nonlinear Programming - Hardcover

Bertsekas, Dimitri P.

Hardcover

ISBN 10: 1886529051 ISBN 13: 9781886529052

Publisher: Athena Scientific, 2016

Synopsis

The third edition of the book is a thoroughly rewritten version of the 1999 2nd edition. New material was included, some of the old material was discarded, and a large portion of the remainder was reorganized or revised.

This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning.

The book was developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization.

Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, large-scale optimization, signal processing, machine learning, and optimal control 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet. Much supplementary/support material can be found at the publisher's and the author's web sites

About this title

About the 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 seventeen 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

"This book contains a wealth of material... Throughout this book, well-prepared graphics illustrate ideas and results. The text contains many examples and each section is followed by a set of nice exercises." --M. Heinkenschloss --Zentralblatt fur Mathematik, October 2000

"This is a beautifully written book by a prolific author ... who has taken painstaking care in making the presentation extremely lucid ... The style is unhurried and intuitive yet mathematically rigorous." "The numerous figures in the book are extremely well thought out and are used in a very effective way to elucidate the text. The detailed and self-explanatory long captions accompanying each figure are extremely helpful." "The 80 pages constituting the four appendixes serve as a masterfully written introduction to the field of nonlinear programming that can be used as a self-contained monograph. Teachers using this book could easily assign these appendixes as introductory or remedial material." --Review by Olvi Mangasarian --Optima, March 1997

This book is a nice combination of classical topics and new important recent developments ... The book contains nice examples and exercises that are included at the end of each section of the chapter to enhance the reader s understanding of the topic. All major proofs are given in full length which in my opinion increases the value of this book as a reference. Each chapter ends with a section of notes and sources, which is very interesting, well written and extremely useful for the readers.
The author develops the material from basic concepts and attempts to make accessible a number of topics that are not often found in textbooks. In the entire book, the presentation style is very clear, unique, compact and easy to follow, but at the same time mathematically rigorous. All the algorithms are clearly explained and presented. The organization of the book makes it possible to use it both as a textbook and as a reference book. Researchers as well as professionals in applied mathematics will also find this book very useful. Overall, this book is an excellent contribution to the field of optimization, and it is highly recommended to the students and researchers in Nonlinear Programming. -- Review by S. Kumar Neogy --Zentralblatt fur Mathematik, 1360, October 2017

Edition details

• Publisher: Athena Scientific
• Publication date: 2016
• ISBN 10: 1886529051
• ISBN 13: 9781886529052
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 861