Title: Optimality Conditions in Convex Optimization : A Finite-Dimensional View Author: Anulekha Dhara, Joydeep Dutta ISBN: 1439868220 / 9781439868225 Format: Hard Cover Pages: 444 Publisher: CRC Press Year: 2011 Availability: Out of Stock
Description
Contents
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