Convex Optimization (eamech691)

By (author) Stephen Boyd; By (author) Boyd, Stephen; By (author) Vandenberghe Lieven
Description:
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Table of contents:
Preface; 1. Introduction; Part I. Theory: 2. Convex sets; 3. Convex functions; 4. Convex optimization problems; 5. Duality; Part II. Applications: 6. Approximation and fitting; 7. Statistical estimation; 8. Geometrical problems; Part III. Algorithms: 9. Unconstrained minimization; 10. Equality constrained minimization; 11. Interior-point methods; Appendices.
Review quote:
''Boyd and Vandenberghe have written a beautiful book that I strongly recommend to everyone interested in optimization and computational mathematics: Convex Optimization is a very readable introduction to this modern field of research.'' Mathematics of Operations Research
Review quote:
''… a beautiful book that I strongly recommend to everyone interested in optimization and computational mathematics … a very readable and inspiring introduction to this modern field of research. I recommend it as one of the best optimization textbooks that have appeared in the last years.'' Mathematical Methods of Operations Research
Review quote:
''I highly recommend it either if you teach nonlinear optimization at the graduate level for a supplementary reading list and for your library, or if you solve optimization problems and wish to know more about solution methods and applications.'' International Statistical institute
Review quote:
''… the whole book is characterized by clarity. … a very good pedagogical book … excellent to grasp the important concepts of convex analysis [and] to develop an art in modelling optimization problems intelligently.'' Matapli
Review quote:
''The book by Boyd and Vandenberghe reviewed here is one of … the best I have ever seen … it is a gentle, but rigorous, introduction to the basic concepts and methods of the field … this book is meant to be a ''first book'' for the student or practitioner of optimization. However, I think that even the experienced researcher in the field has something to gain from reading this book: I have very much enjoyed the easy to follow presentation of many meaningful examples and suggestive interpretations meant to help the student''s understanding penetrate beyond the surface of the formal description of the concepts and techniques. For teachers of convex optimization this book can be a gold mine of exercises. MathSciNet
Biographical note:
Stephen Boyd received his PhD from the University of California, Berkeley. Since 1985 he has been a member of the Electrical Engineering Department at Stanford University, where he is now Professor and Director of the Information Systems Laboratory. He has won numerous awards for teaching and research, and is a Fellow of the IEEE. He was one of the co-founders of Barcelona Design, and is the co-author of two previous books Linear Controller Design: Limits of Performance and Linear M