Convex Optimization

A comprehensive introduction to the tools, techniques and applications of convex optimization.

Stephen Boyd (Author), Lieven Vandenberghe (Author)

9780521833783, Cambridge University Press

Hardback, published 8 March 2004

727 pages, 337 exercises
25.4 x 19.7 x 4 cm, 1.68 kg

'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

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.

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.

Subject Areas: Computer science [UY], Electronics & communications engineering [TJ], Optimization [PBU], Mathematics [PB], Investment & securities [KFFM], Econometrics [KCH]