- Title
- Subdifferential of the supremum function : moving back and forth between continuous and non-continuous settings
- Creator
- Correa, Rafael; Hantoute, Abderrahim; Lopez, Marco
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/186135
- Identifier
- vital:16811
- Identifier
-
https://doi.org/10.1007/s10107-020-01592-0
- Identifier
- ISBN:0025-5610 (ISSN)
- Abstract
- In this paper we establish general formulas for the subdifferential of the pointwise supremum of convex functions, which cover and unify both the compact continuous and the non-compact non-continuous settings. From the non-continuous to the continuous setting, we proceed by a compactification-based approach which leads us to problems having compact index sets and upper semi-continuously indexed mappings, giving rise to new characterizations of the subdifferential of the supremum by means of upper semicontinuous regularized functions and an enlarged compact index set. In the opposite sense, we rewrite the subdifferential of these new regularized functions by using the original data, also leading us to new results on the subdifferential of the supremum. We give two applications in the last section, the first one concerning the nonconvex Fenchel duality, and the second one establishing Fritz-John and KKT conditions in convex semi-infinite programming. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.
- Publisher
- Springer Science and Business Media Deutschland GmbH
- Relation
- Mathematical Programming Vol. 189, no. 1-2 (2021), p. 217-247; http://purl.org/au-research/grants/arc/DP180100602
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2020, Springer-Verlag GmbH
- Rights
- Open Access
- Subject
- 4613 Theory of computation; 4901 Applied mathematics; 4903 Numerical and computational mathematics; Convex semi-infinite programming; Fritz-John and KKT optimality conditions; Stone–Čech compactification; Subdifferentials; Supremum of convex functions
- Full Text
- Reviewed
- Funder
- Research supported by CONICYT (Fondecyt 1190012 and 1190110), Proyecto/Grant PIA AFB-170001, MICIU of Spain and Universidad de Alicante (Grant Beatriz Galindo BEAGAL 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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