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
Promotions
|
| LSN: |
0-387-28719-1 |
| Barcode: |
9780387287195 |
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