Primal–Dual Optimization Conditions for the Robust Sum of Functions with Applications
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Título: | Primal–Dual Optimization Conditions for the Robust Sum of Functions with Applications |
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Autor/es: | Dinh, Nguyen | Goberna, Miguel 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: | Robust sum function | Duality | Optimality conditions | Existence of optimal solutions | Inconsistent convex inequality systems best approximation |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 25-jul-2019 |
Editor: | Springer US |
Cita bibliográfica: | Applied Mathematics & Optimization. 2019, 80(3): 643-664. doi:10.1007/s00245-019-09596-9 |
Resumen: | This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in Dinh et al. (Set Valued Var Anal, 2019). It provides an existence theorem for primal optimal solutions and, under suitable duality assumptions, characterizations of the primal–dual optimal set, the primal optimal set, and the dual optimal set, as well as a formula for the subdifferential of the robust sum function. The mentioned results are applied to get simple formulas for the robust sums of subaffine functions (a class of functions which contains the affine ones) and to obtain conditions guaranteeing the existence of best approximate solutions to inconsistent convex inequality systems. |
Patrocinador/es: | This research was supported by the National Foundation for Science and Technology Development (NAFOSTED), Vietnam, Project 101.01-2018.310 Some topics on systems with uncertainty and robust optimization, and by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Project PGC2018-097960-B-C22. |
URI: | http://hdl.handle.net/10045/97528 |
ISSN: | 0095-4616 (Print) | 1432-0606 (Online) |
DOI: | 10.1007/s00245-019-09596-9 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1007/s00245-019-09596-9 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas |
Archivos en este ítem:
Archivo | Descripción | Tamaño | Formato | |
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2019_Dinh_etal_ApplMathOptim_final.pdf | Versión final (acceso restringido) | 358,71 kB | Adobe PDF | Abrir Solicitar una copia |
2019_Dinh_etal_ApplMathOptim_revised.pdf | Versión revisada (acceso abierto) | 1,05 MB | Adobe PDF | Abrir Vista previa |
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