Convex Optimization
Stephen Boyd: Stanford University, California
Lieven Vandenberghe: University of California, Los Angeles
ISBN-10: 0521833787
ISBN-13: 9780521833783
Published March 2004
730 pages
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.
• Gives comprehensive details on how to recognize convex optimization problems in a wide variety of settings
• Provides a broad range of practical algorithms for solving real problems
• Contains hundreds of worked examples and homework exercises
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.
Reviews
'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
'… 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
'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
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