New glimpses on convex infinite optimization duality
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Título: | New glimpses on convex infinite optimization duality |
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Autor/es: | Goberna, Miguel A. | López Cerdá, Marco A. | Volle, Michel |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Convex infinite programming | Duality |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | sep-2015 |
Editor: | Springer Milan |
Cita bibliográfica: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2015, 109(2): 431-450. doi:10.1007/s13398-014-0194-2 |
Resumen: | Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described. |
Patrocinador/es: | M. A. Goberna and M. A. López were partially supported by MINECO of Spain, Grant MTM2011-29064-C03-02. |
URI: | http://hdl.handle.net/10045/51991 |
ISSN: | 1578-7303 (Print) | 1579-1505 (Online) |
DOI: | 10.1007/s13398-014-0194-2 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © Springer-Verlag Italia 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s13398-014-0194-2 |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1007/s13398-014-0194-2 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
Archivos en este ítem:
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2015_Goberna_etal_RACSAM_final.pdf | Versión final (acceso restringido) | 424,68 kB | Adobe PDF | Abrir Solicitar una copia |
2015_Goberna_etal_RACSAM_preprint.pdf | Preprint (acceso abierto) | 217,24 kB | Adobe PDF | Abrir Vista previa |
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