Alternative Representations of the Normal Cone to the Domain of Supremum Functions and Subdifferential Calculus
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Título: | Alternative Representations of the Normal Cone to the Domain of Supremum Functions and Subdifferential Calculus |
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Autor/es: | Correa, Rafael | Hantoute, Abderrahim | López Cerdá, Marco A. |
Grupo/s de investigación o GITE: | Laboratorio de Optimización (LOPT) |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemáticas |
Palabras clave: | Normal cone | Supremum of convex functions | Subdifferentials | Convex optimization | Optimality conditions |
Área/s de conocimiento: | Estadística e Investigación Operativa |
Fecha de publicación: | 26-abr-2021 |
Editor: | Springer Nature |
Cita bibliográfica: | Set-Valued and Variational Analysis. 2021, 29: 683-699. https://doi.org/10.1007/s11228-021-00583-3 |
Resumen: | The first part of the paper provides new characterizations of the normal cone to the effective domain of the supremum of an arbitrary family of convex functions. These results are applied in the second part to give new formulas for the subdifferential of the supremum function, which use both the active and nonactive functions at the reference point. Only the data functions are involved in these characterizations, the active ones from one side, together with the nonactive functions multiplied by some appropriate parameters. In contrast with previous works in the literature, the main feature of our subdifferential characterization is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of this domain) does not appear. A new type of optimality conditions for convex optimization is established at the end of the paper. |
Patrocinador/es: | Research supported by ANID (Fondecyt 1190012 and 1190110), Proyecto CMM ANID PIA AFB170001, MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA-GAL 18/00205), and Research Project PGC2018-097960-B-C21 from MICINN, Spain. The research of the third author is also supported by the Australian ARC -Discovery Projects DP 180100602. |
URI: | http://hdl.handle.net/10045/115194 |
ISSN: | 1877-0533 (Print) | 1877-0541 (Online) |
DOI: | 10.1007/s11228-021-00583-3 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © The Author(s), under exclusive licence to Springer Nature B.V. 2021 |
Revisión científica: | si |
Versión del editor: | https://doi.org/10.1007/s11228-021-00583-3 |
Aparece en las colecciones: | INV - LOPT - Artículos de Revistas INV - GAM - Artículos de Revistas |
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Correa_etal_2021_Set-ValuedVarAnal_preprint.pdf | Preprint (acceso abierto) | 239,03 kB | Adobe PDF | Abrir Vista previa |
Correa_etal_2021_Set-ValuedVarAnal_final.pdf | Versión final (acceso restringido) | 353,9 kB | Adobe PDF | Abrir Solicitar una copia |
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