- Title
- Subdifferential of the supremum via compactification of the index set
- Creator
- Correa, Rafael; Hantoute, Abderrahim; López, Marco
- Date
- 2020
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/173303
- Identifier
- vital:14645
- Identifier
-
https://doi.org/10.1007/s10013-020-00403-5
- Identifier
- ISBN:2305-221X (ISSN)
- Abstract
- 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. © 2020, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.; Funding details: Fondo Nacional de Desarrollo CientÃfico, Tecnológico y de Innovación Tecnológica, FONDECYT, PIA AFB-170001, 1190110, 1190012 Funding details: Universidad de Alicante, BEA- GAL 18/00205, PGC2018-097960-B-C21 Funding details: Australian Research Council, ARC, DP 180100602 Funding details: Comisión Nacional de Investigación CientÃfica y Tecnológica, CONICYT Funding details: Ministerio de Ciencia e Innovación, MICINN Funding text 1: 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
- Publisher
- Springer
- Relation
- Vietnam Journal of Mathematics Vol. 48, no. 3 (2020), p. 569-588, http://purl.org/au-research/grants/arc/DP180100602
- Rights
- Copyright © Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2020
- Rights
- This metadata is freely available under a CCO license
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Convex semi-infinite programming; Optimality conditions; Stone–Čech compactification; Subdifferentials; Supremum of convex functions
- Full Text
- Reviewed
- Funder
- Funding details: Fondo Nacional de Desarrollo CientÃfico, Tecnológico y de Innovación Tecnológica, FONDECYT, PIA AFB-170001, 1190110, 1190012 Funding details: Universidad de Alicante, BEA- GAL 18/00205, PGC2018-097960-B-C21 Funding details: Australian Research Council, ARC, DP 180100602 Funding details: Comisión Nacional de Investigación CientÃfica y Tecnológica, CONICYT Funding details: Ministerio de Ciencia e Innovación, MICINN Funding text 1: 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
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