Convexity and Well-Posed Problems - Rilegato

Lucchetti, Roberto

Rilegato

ISBN 10: 0387287191 ISBN 13: 9780387287195

Casa editrice: Springer-Verlag GmbH, 2005

Riassunto

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. 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.

Su questo libro

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.

Dettagli dell'edizione

• Editore: Springer-Verlag GmbH
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0387287191
• ISBN 13: 9780387287195
• Rilegatura: Copertina rigida
• Numero di pagine: 305
• Contatto del produttore: Springer-Verlag GmbH; customerservice@springernature.com; ; Tiergartenstraße 17; Heidelberg; Baden-Württemberg; 69121; Germania