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.

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.

��ber diesen Titel� kann sich auf eine andere Ausgabe dieses Titels beziehen.

Anbieterinformationen

Australian Book seller. Weide varierty of fiction and non-fiction books

Zur Homepage des Verk�ufers

Unternehmensdaten des Verk�ufers

sadia zaki
21, harriet court, Salisbury Plain, SA, 5107, Australia

Gesch�ftsbedingungen und Versandinformationen

Verkaufsbedingungen

Ships from Australia and USA

Widerrufsbelehrung

Versandbedingungen

Shipping rates are for 1 KG book. For heavy items additional charges may be requested

Versandkosten von Australien nach Deutschland

Versandkosten von Australien nach Deutschland
Bestellmenge	8 bis 18�Werktage	4 bis 8�Werktage
Erster Artikel	EUR 0.00	EUR 12.81

Die Versandzeiten werden von den Verk�uferinnen und Verk�ufern festgelegt. Sie variieren je nach Versanddienstleister und Standort. Sendungen, die den Zoll passieren, k�nnen Verz�gerungen unterliegen. Eventuell anfallende Abgaben oder Geb�hren sind von der K�uferin bzw. dem K�ufer zu tragen. Die Verk�uferin bzw. der Verk�ufer kann Sie bez�glich zus�tzlicher Versandkosten kontaktieren, um einen m�glichen Anstieg der Versandkosten f�r Ihre Artikel auszugleichen.