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