Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature—notably in the area of convex analysis—essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory.
Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.
Chapter 1 : What Is Convex Optimization?
Chapter 2 : Tools for Convex Optimization
Chapter 3 : Convex Functions
Chapter 4 : Basic Optimality Conditions using the Normal Cone
Chapter 5 : Saddle Points, Optimality, and Duality
Chapter 6 : Enhanced Fritz John Optimality Conditions
Chapter 7 : Optimality without Constraint Qualification
Chapter 8 : Sequential Optimality Conditions and Generalized Constraint Qualification
Chapter 9 : Representation of the Feasible Set and KKT Conditions
Chapter 10 : Weak Sharp Minima in Convex Optimization
Chapter 11 : Approximate Optimality Conditions
Chapter 12 : Convex Semi-Infinite Optimization
Chapter 13 : Convexity in Nonconvex Optimization
Bibliography
Index
