On the stable containment of two sets
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Título: | On the stable containment of two sets |
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Autor/es: | Goberna, Miguel A. | Vera de Serio, Virginia N. |
Grupo/s de investigación o GITE: | Programación Semi-infinita |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad Nacional de Cuyo. Facultad de Económicas |
Palabras clave: | Stability theory | Containment problem | Set-valued mappings | Semi-infinite systems |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 30-ene-2008 |
Editor: | Springer |
Cita bibliográfica: | GOBERNA TORRENT, Miguel Ángel; VERA DE SERIO, Virginia N. "On the stable containment of two sets". Journal of Global Optimization. Vol. 41, No. 4 (2008). ISSN 0925-5001, pp. 613-624 |
Resumen: | This paper studies the stability of the set containment problem. Given two non-empty sets in the Euclidean space which are the solution sets of two systems of (possibly infinite) inequalities, the Farkas type results allow to decide whether one of the two sets is contained or not in the other one (which constitutes the so-called containment problem). In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the two sets is preserved by sufficiently small perturbations or not. This paper deals with this stability problem as a particular case of the maintaining of the relative position of the images of two set-valued mappings; first for general set-valued mappings and second for solution sets mappings of convex and linear systems. Thus the results in this paper could be useful in the postoptimal analysis of optimization problems with inclusion constraints. |
Patrocinador/es: | Research supported by MCYT of Spain and FEDER of EU, Grant MTM2005-08572-C03-01, and by SECYT-UNCuyo of Argentina, Grant 658/05-R, 882/07-R. |
URI: | http://hdl.handle.net/10045/15412 |
ISSN: | 0925-5001 (Print) | 1573-2916 (Online) |
DOI: | 10.1007/s10898-007-9276-4 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | The original publication is available at www.springerlink.com |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1007/s10898-007-9276-4 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
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Goberna_On_the_stable_Rev.pdf | Versión revisada (acceso libre) | 151,23 kB | Adobe PDF | Abrir Vista previa |
Goberna_On_the_stable_Final.pdf | Versión final (acceso restringido) | 190,57 kB | Adobe PDF | Abrir Solicitar una copia |
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