- Title
- New tour on the subdifferential of supremum via finite sums and suprema
- Creator
- Hantoute, Abderrahim; López-Cerdá, Marco
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/186831
- Identifier
- vital:16965
- Identifier
-
https://doi.org/10.1007/s10957-021-01925-9
- Identifier
- ISBN:0022-3239 (ISSN)
- Abstract
- This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family. © 2021, The Author(s).
- Publisher
- Springer
- Relation
- Journal of Optimization Theory and Applications Vol. 193, no. 1-3 (2022), p. 81-106
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021, The Author(s)
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; Normal cones; Subdifferentials; Supremum of convex functions
- Full Text
- Reviewed
- Funder
- The research of the first author is supported by ANID-Fondecyt 1190012, Proyecto/Grant PIA AFB-170001, MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA- GAL 18/00205). The second author is supported by the Research Project PGC2018-097960-B-C21 from MICINN, Spain, and by the Australian ARC—Discovery Projects DP 180100602.
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