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 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.