Convexity and Well-Posed Problems (CMS Books in Mathematics) - Tapa blanda

Lucchetti, Roberto

 
9781441921116: Convexity and Well-Posed Problems (CMS Books in Mathematics)
Tapa blanda
ISBN 10: 1441921117 ISBN 13: 9781441921116
Editorial: Springer, 2010

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

De la contraportada

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.

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Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
1441921117
ISBN 13 
9781441921116
Encuadernación
Tapa blanda
Número de páginas
320
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9780387287195: Convexity and Well-Posed Problems (CMS Books in Mathematics)

Edición Destacada

ISBN 10:  0387287191 ISBN 13:  9780387287195
Editorial: Springer, 2005
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