Convexity and Well-Posed Problems

by Roberto Lucchetti

Overview

This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is defined to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it.

Product Details

ISBN-13:	9780387287195
Publisher:	Springer New York
Publication date:	11/16/2005
Series:	CMS Books in Mathematics
Edition description:	2006
Pages:	305
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Convex sets and convex functions: the fundamentals.- Continuity and—(X).- The derivatives and the subdifferential.- Minima and quasi minima.- The Fenchel conjugate.- Duality.- Linear programming and game theory.- Hypertopologies, hyperconvergences.- Continuity of some operations between functions.- Well-posed problems.- Generic well-posedness.- More exercises.

Editorial Reviews

From the reviews:

"In this book the author focuses on the study of convex functions and their properties under perturbations of data. In particular, he illustrates the ideas of stability and well-posedness and the connections between them. … This book is intended for graduate students and researchers especially in mathematics, physics and economics; to facilitate its use as a textbook, the author has included many exercises and examples of different levels of difficulty." (Davide La Torre, Mathematical Reviews, Issue 2006 h)

"This book studies convex functions in Banach spaces and the stable behavior under perturbations of the optimization problems associated to them. … An interesting feature of the book is the inclusion of some topics, like elements of game theory, hypertopologies and genericity of well-posedness, not usually found in textbooks devoted to convexity and optimization. … several useful examples, comments and remarks scattered throughout, and over 120 exercises of varying level difficulty. This book is suitable for graduate courses on convex optimization from a mathematical standpoint." (Tullio Zolezzi, Zentralblatt MATH, Vol. 1106 (8), 2007)

From the Publisher