Convex Optimization

"Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, covering the theory, many applications and examples, and numerical methods. The book begins with the basic elements of convex sets and functions, describes various classes of convex optimization problems, and then treats duality theory. The second part covers a wide variety of applications, in estimation, approximation, statistics, computational geometry, and other areas. The last part of the book presents numerical methods for convex optimization problems, moving from basic methods for unconstrained problems to interior-point methods. The focus of the book is on recognizing and formulating convex optimization problems, and then solving them efficiently. It contains many worked examples and homework exercises and will appeal to students, researchers, and practitioners in fields such as engineering, computer science, mathematics, finance, and economics. From the publisher. 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 Introduction -- I Theory: Introduction -- I Theory: Introduction -- I Theory: Introduction -- I Theory: Introduction -- I Theory: -- II Applications: Introduction -- I Theory: -- II Applications: Introduction -- I Theory: -- II Applications: Introduction -- I Theory: -- II Applications: -- III Algorithms: Introduction -- I Theory: -- II Applications: -- III Algorithms: Introduction -- I Theory: -- II Applications: -- III Algorithms: Introduction -- I Theory: -- II Applications: -- III Algorithms: -- Appendices: A. Introduction -- I Theory: -- II Applications: -- III Algorithms: -- Appendices: A. -- B. Introduction -- I Theory: -- II Applications: -- III Algorithms: -- Appendices: A. -- B. -- C. Introduction-- I Theory:-- II Applications:-- III Algorithms:-- Appendices: A.-- B.-- C. Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text 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. In this introduction we give an overview of mathematical optimization, focusing on the special role of convex optimization.