Functional Inequalities in the Absence of Convexity and Lower Semicontinuity with Applications to Optimization
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Título: | Functional Inequalities in the Absence of Convexity and Lower Semicontinuity with Applications to Optimization |
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Autor/es: | Dinh, Nguyen | 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: | Functional inequalities | Farkas-type lemmas for nonconvex systems | Infinite-dimensional nonconvex optimization |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 6-jul-2010 |
Editor: | Society for Industrial and Applied Mathematics (SIAM) |
Cita bibliográfica: | SIAM Journal on Optimization. 2010, 20(5): 2540-2559. doi:10.1137/09077552X |
Resumen: | In this paper we extend some results in [Dinh, Goberna, López, and Volle, Set-Valued Var. Anal., to appear] to the setting of functional inequalities when the standard assumptions of convexity and lower semicontinuity of the involved mappings are absent. This extension is achieved under certain condition relative to the second conjugate of the involved functions. The main result of this paper, Theorem 1, is applied to derive some subdifferential calculus rules and different generalizations of the Farkas lemma for nonconvex systems, as well as some optimality conditions and duality theory for infinite nonconvex optimization problems. Several examples are given to illustrate the significance of the main results and also to point out the potential of their applications to get various extensions of Farkas-type results and to the study of other classes of problems such as variational inequalities and equilibrium models. |
Patrocinador/es: | This research was partially supported by MICINN of Spain, grant MTM2008-06695-C03-01. |
URI: | http://hdl.handle.net/10045/75129 |
ISSN: | 1052-6234 (Print) | 1095-7189 (Online) |
DOI: | 10.1137/09077552X |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2010 Society for Industrial and Applied Mathematics |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1137/09077552X |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
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2010_Dinh_etal_SIAMJOptim.pdf | 222,65 kB | Adobe PDF | Abrir Vista previa | |
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