Convex Representatives of the Value Function and Aumann Integrals in Normed Spaces
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Título: | Convex Representatives of the Value Function and Aumann Integrals in Normed Spaces |
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Autor/es: | Flores-Bazán, Fabián | Hantoute, Abderrahim |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Value function | Nonconvex optimization | Bochner, Pettis, and Gelfand integrals | Convex representative functions | Positively homogeneous problems |
Fecha de publicación: | 15-nov-2022 |
Editor: | Society for Industrial and Applied Mathematics (SIAM) |
Cita bibliográfica: | SIAM Journal on Optimization. 2022, 32(4): 2773-2796. https://doi.org/10.1137/22M1471377 |
Resumen: | Convex representatives are proposed for the value function of an infinite-dimensional constrained nonconvex variational problem. All the involved variables in this problem take their values in (possibly of infinite dimension, not necessarily separable or complete) normed spaces, while the associated measure can be any σ-finite, nonnegative, and nonatomic complete measure. This in particular shows that the closure hull of the (possibly nonconvex) value function is always convex, as long as the sense of the integral within the cone-valued functional constraint is given and the type of the closure is appropriately determined. Correspondingly, similar convexity properties for the Aumann integral in general normed spaces of infinite dimension are established. Applications are given in a fairly general positively homogeneous framework. |
Patrocinador/es: | This work was supported by ANID Fondecyt, grants 1212004, 1190012, ACE210010, and Basal FB210005, by the MICIU of Spain and Universidad de Alicante (contract Beatriz Galindo BEA-GAL 18/00205), and by research projects PGC2018-097960-B-C21 from MICINN of Spain and AICO/2021/165 of Generalitat Valenciana. |
URI: | http://hdl.handle.net/10045/130325 |
ISSN: | 1052-6234 (Print) | 1095-7189 (Online) |
DOI: | 10.1137/22M1471377 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2022 Society for Industrial and Applied Mathematics |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1137/22M1471377 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas INV - GAM - Artículos de Revistas |
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Flores-Bazan_Hantoute_2022_SIAMJOptim_final.pdf | 441,55 kB | Adobe PDF | Abrir Vista previa | |
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