Optimality Conditions in Convex Optimization : A Finite-Dimensional View

Covering the current state of the art, this book explores an important and central issue in convex optimization: optimality conditions. Although many results presented in the chapters can also be proved in infinite dimensions, the text focuses on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. The authors include examples wherever needed, details of major results, and proofs of the main results.

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.