Duality for Nonconvex Approximation and Optimization

The theory of convex optimization has been developing constantly over the past 30 years. Recently, researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimization problems. This monograph contains an exhaustive presentation of the duality theory for these classes of problems and their generalizations.

Contains the latest results (most recent related book was published almost 5 years ago) Reviews new and sophisticated variations capping 3 decades of progress in the field Provides a comprehensive analysis of so-called "anticonvex" and "convex-anticonvex" optimization problems An exhaustive presentation of the duality theory for these classes of problems and their generalizations

Klappentext

The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

Inhalt
Preliminaries.- Worst Approximation.- Duality for Quasi-convex Supremization.- Optimal Solutions for Quasi-convex Maximization.- Reverse Convex Best Approximation.- Unperturbational Duality for Reverse Convex Infimization.- Optimal Solutions for Reverse Convex Infimization.- Duality for D.C. Optimization Problems.- Duality for Optimization in the Framework of Abstract Convexity.- Notes and Remarks.