Subdifferential of the Supremum via Compactification of the Index Set
| Autor: | Abderrahim Hantoute, Marco A. López, Rafael Correa Fontecilla |
|---|---|
| Přispěvatelé: | Universidad de Alicante. Departamento de Matemáticas, Laboratorio de Optimización (LOPT) |
| Rok vydání: | 2020 |
| Předmět: |
Subdifferentials
Optimality conditions 021103 operations research Convex semi-infinite programming Supremum of convex functions General Mathematics 010102 general mathematics 0211 other engineering and technologies 02 engineering and technology Subderivative Stone– Čech compactification 01 natural sciences Infimum and supremum Combinatorics Estadística e Investigación Operativa Stone–Čech compactification Compactification (mathematics) 0101 mathematics Mathematics |
| Zdroj: | Vietnam Journal of Mathematics. 48:569-588 |
| ISSN: | 2305-2228 2305-221X |
| DOI: | 10.1007/s10013-020-00403-5 |
| Popis: | We give new characterizations for the subdifferential of the supremum of an arbitrary family of convex functions, dropping out the standard assumptions of compactness of the index set and upper semi-continuity of the functions with respect to the index (J. Convex Anal. 26, 299–324, 2019). We develop an approach based on the compactification of the index set, giving rise to an appropriate enlargement of the original family. Moreover, in contrast to the previous results in the literature, our characterizations are formulated exclusively in terms of exact subdifferentials at the nominal point. Fritz–John and KKT conditions are derived for convex semi-infinite programming. Research supported by CONICYT (Fondecyt 1190012 and 1190110), Proyecto/Grant PIA AFB-170001, MICIU of Spain and Universidad de Alicante (Grant 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. |
| Databáze: | OpenAIRE |
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