Convexity and Well-Posed Problems (Hardcover, 2006 ed.)

This book deals with the study of convex functions and of their behavior from the point of view of stability with respect to perturbations. Convex functions are considered from the modern point of view that underlines the geometrical aspect: thus a function is defined as convex whenever its graph is a convex set.

A primary goal of this book is to study the problems of stability and well-posedness, in the convex case. Stability means that the basic parameters of a minimum problem do not vary much if we slightly change the initial data. On the other hand, well-posedness means that points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of functions and of sets. This approach fits perfectly with the idea of regarding functions as sets. Thus the second part of the book starts with a short, yet rather complete, overview of the so-called hypertopologies, i.e. topologies in the closed subsets of a metric space.

While there exist numerous classic texts on the issue of stability, there only exists one book on hypertopologies [Beer 1993]. The current book differs from Beera (TM)s in that it contains a much more condensed explication of hypertopologies and is intended to help those not familiar with hypertopologies learn how to use them in the context of optimization problems.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	CMS Books in Mathematics
Release date:	November 2005
First published:	2006
Authors:	Roberto Lucchetti
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	305
Edition:	2006 ed.
ISBN-13:	978-0-387-28719-5
Categories:	Books > Science & Mathematics > Mathematics > Geometry > General
LSN:	0-387-28719-1
Barcode:	9780387287195

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