Duality for Nonconvex Approximation and Optimization [Hardcover]

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.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.

From the reviews:

Being the first monograph devoted to nonconvex duality, this book is going to become a fundamental source for researchers in the field. An important feature of the book is that it is also accessible to nonspecialists, since, in spite of dealing with a rather specialized topic, it is essentially self-contained. & this monograph is a very useful addition to the existing literature on optimization and approximation and is undoubtedly going to constitute a major reference on nonconvex duality. (Juan-Enrique Martinez-Legaz, Mathematical Reviews, Issue 2006 k)

This monograph, being the first book of this kind in the literature, covers a wide range of optimization and approximation problems. It provides an excellent overview over the literature and, moreover, it contains a lot of new results and new proofs of known results. The results and the choice of the classes of problems are well motivated. & The monograph is appló„