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Convexity and Well-Posed Problems
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,...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2006.
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| Edición: | 1st ed. 2006. |
| Colección: | CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-0-387-31082-4 | ||
| 003 | DE-He213 | ||
| 005 | 20220118032458.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2006 xxu| s |||| 0|eng d | ||
| 020 | |a 9780387310824 |9 978-0-387-31082-4 | ||
| 024 | 7 | |a 10.1007/0-387-31082-7 |2 doi | |
| 050 | 4 | |a QA402.5-402.6 | |
| 050 | 4 | |a QA315-316 | |
| 072 | 7 | |a PBU |2 bicssc | |
| 072 | 7 | |a MAT005000 |2 bisacsh | |
| 072 | 7 | |a PBU |2 thema | |
| 082 | 0 | 4 | |a 519.6 |2 23 |
| 082 | 0 | 4 | |a 515.64 |2 23 |
| 100 | 1 | |a Lucchetti, Roberto. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Convexity and Well-Posed Problems |h [electronic resource] / |c by Roberto Lucchetti. |
| 250 | |a 1st ed. 2006. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2006. | |
| 300 | |a XIV, 305 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, |x 2197-4152 | |
| 505 | 0 | |a Convex sets and convex functions: the fundamentals -- Continuity and ?(X) -- The derivatives and the subdifferential -- Minima and quasi minima -- The Fenchel conjugate -- Duality -- Linear programming and game theory -- Hypertopologies, hyperconvergences -- Continuity of some operations between functions -- Well-posed problems -- Generic well-posedness -- More exercises. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Calculus of variations. | |
| 650 | 0 | |a Operations research. | |
| 650 | 0 | |a Management science. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Calculus of Variations and Optimization. |
| 650 | 2 | 4 | |a Operations Research, Management Science . |
| 650 | 2 | 4 | |a Functional Analysis. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9780387509372 |
| 776 | 0 | 8 | |i Printed edition: |z 9781441921116 |
| 776 | 0 | 8 | |i Printed edition: |z 9780387287195 |
| 830 | 0 | |a CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, |x 2197-4152 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/0-387-31082-7 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||