Inhaltsangabe
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.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Von der hinteren Coverseite
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.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
Weitere beliebte Ausgaben desselben Titels
Suchergebnisse für Convexity and Well-Posed Problems (CMS Books in Mathematics)
Beispielbild für diese ISBN
Convexity and Well-Posed Problems
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
Paperback. Zustand: Brand New. 305 pages. 9.00x6.00x0.73 inches. In Stock. Artikel-Nr. x-1441921117
Neu kaufen
EUR 79,82
Versand:
EUR 14,19
Von Vereinigtes Königreich nach USA
Anzahl: 2 verfügbar
Foto des Verkäufers
Convexity and Well-Posed Problems
Anbieter: preigu, Osnabrück, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: Neu. Convexity and Well-Posed Problems | Roberto Lucchetti | Taschenbuch | xiv | Englisch | 2010 | Springer | EAN 9781441921116 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Artikel-Nr. 107253168
Neu kaufen
EUR 49,15
Versand:
EUR 70,00
Von Deutschland nach USA
Anzahl: 5 verfügbar
Foto des Verkäufers
Convexity and Well-Posed Problems
Verlag:
Springer US, Springer New York, 2010
ISBN 10: 1441921117
ISBN 13: 9781441921116
Neu
Taschenbuch
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9781441921116
Neu kaufen
EUR 58,55
Versand:
EUR 62,44
Von Deutschland nach USA
Anzahl: 1 verfügbar