Optimality Conditions in Convex Optimization: A Finite-Dimensional View [Paperback]

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 literaturenotably in the area of convex analysisessential 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.

What Is Convex Optimization?. Tools for Convex Optimization. Basic Optimality Conditions using the Normal Cone. Saddle Points, Optimality and Duality. Enhanced Fritz John Optimality Conditions. Optimality without Constraint Qualification. Sequential Optimality Conditions and Generalized Constraint Qualification. Representation of the Feasible Set and KKT Conditions. Weak Sharp Minima in Convex Optimization. Approximate Optimality Conditions. Convex Semi-infinite Optimization. Convexity in Non-Convex Optimization. Bibliography. Index.

This book explores an extremely important issue in convex optimization: optimality conditions. The text focuses on finite dimensions to allow for much deeper results alÓ>