Details

Duality for Nonconvex Approximation and Optimization

CMS Books in Mathematics

von: Ivan Singer
96,29 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	12.03.2007
ISBN/EAN:	9780387283951
Sprache:	englisch
Anzahl Seiten:	356

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Beschreibungen

Inhaltsverzeichnis

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.

Back cover copy

In this monograph the author presents the theory of duality for
nonconvex approximation in normed linear spaces and nonconvex global
optimization in locally convex spaces. Key topics include:
* duality for worst approximation (i.e., the maximization of the
distance of an element to a convex set)
* duality for reverse convex best approximation (i.e., the minimization of
the distance of an element to the complement of a convex set)
* duality for convex maximization (i.e., the maximization of a convex
function on a convex set)
* duality for reverse convex minimization (i.e., the minimization of a
convex function on the complement of a convex set)
* duality for d.c. optimization (i.e., optimization problems involving
differences of convex functions).
Detailed proofs of results are given, along with varied illustrations.
While many of the results have been published in mathematical journals,
this is the first time these results appear in book form. In
addition, unpublished results and new proofs are provided. This
monograph should be of great interest to experts in this and related
fields.
Ivan Singer is a Research Professor at the Simion Stoilow Institute of
Mathematics in Bucharest, and a Member of the Romanian Academy. He is
one of the pioneers of approximation theory in normed linear spaces, and
of generalizations of approximation theory to optimization theory. He
has been a Visiting Professor at several universities in the U.S.A.,
Great Britain, Germany, Holland, Italy, and other countries, and was the
principal speaker at an N. S. F. Regional Conference at Kent State
University. He is one of the editors of the journals Numerical
Functional Analysis and Optimization (since its inception in 1979),
Optimization, and Revue d'analyse num\'erique et de th\'eorie de
l'approximation. His previous books include Best Approximation in
Normed Linear Spaces by Elements of Linear Subspaces (Springer 1970),
The Theory of Best Approximation and Functional Analysis (SIAM 1974), Bases
in Banach Spaces I, II (Springer, 1970, 1981), and Abstract Convex Analysis
(Wiley-Interscience, 1997).

Sonderbeitrag

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

Verkaufsargumente

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.