Convexity and Well-Posed Problems

Lucchetti, Roberto

ISBN 10: 1441921117 / ISBN 13: 9781441921116

Editore: Springer-Verlag New York Inc., 2010

Series: CMS Books in Mathematics. Num Pages: 319 pages, biography. BIC Classification: PBKB; PBKQ; PBUH. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 17. Weight in Grams: 492. . 2010. Softcover reprint of hardcover 1st ed. 2006. paperback. . . . . Books ship from the US and Ireland. Codice articolo V9781441921116

Riassunto:

This book studies the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data, while well-posedness means 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 book contains a 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.

Dalla quarta di copertina:

Intended for graduate students especially in mathematics, physics, and

economics, this book deals with the study of convex functions and of

their behavior from the point of view of stability with respect to

perturbations. The primary goal is the study of the problems of

stability and well-posedness, in the convex case. Stability means the

basic parameters of a minimum problem do not vary much if we slightly

change the initial data. 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

both functions and of sets.

The book includes a discussion of numerous topics, including:

* hypertopologies, ie, topologies on the closed subsets of a metric space;

* duality in linear programming problems, via cooperative game theory;

* the Hahn-Banach theorem, which is a fundamental tool for the study of convex functions;

* questions related to convergence of sets of nets;

* genericity and porosity results;

* algorithms for minimizing a convex function.

In order to facilitate use as a textbook, the author has included a

selection of examples and exercises, varying in degree of difficulty.

Robert Lucchetti is Professor of Mathematics at Politecnico di Milano. He has taught this material to graduate students at his own university, as well as the Catholic University of Brescia, and the University of Pavia.

Dati bibliografici

Titolo: Convexity and Well-Posed Problems
Casa editrice: Springer-Verlag New York Inc.
Data di pubblicazione: 2010
Legatura: Brossura
Condizione: New