Convexity and Well-Posed Problems (Paperback, Softcover reprint of hardcover 1st ed. 2006)

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 de?ned 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. Moreover, we shall consider extended real valued functions, i. e. , functions taking possibly the values?? and +?. The reason for considering the value +? is the powerful device of including the constraint set of a constrained minimum problem into the objective function itself (by rede?ning it as +? outside the constraint set). Except for trivial cases, the minimum value must be taken at a point where the function is not +?, hence at a point in the constraint set. And the value ?? is allowed because useful operations, such as the inf-convolution, can give rise to functions valued?? even when the primitive objects are real valued. Observe that de?ning the objective function to be +? outside the closed constraint set preserves lower semicontinuity, which is the pivotal and mi- mal continuity assumption one needs when dealing with minimum problems. Variational calculus is usually based on derivatives.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	CMS Books in Mathematics
Release date:	November 2010
First published:	2006
Authors:	Roberto Lucchetti
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Paperback
Pages:	305
Edition:	Softcover reprint of hardcover 1st ed. 2006
ISBN-13:	978-1-4419-2111-6
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Optimization > Linear programming
LSN:	1-4419-2111-7
Barcode:	9781441921116

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