- Title
- Alternative representations of the normal cone to the domain of supremum functions and subdifferential calculus
- Creator
- Correa, Rafael; Hantoute, Abderrahim; Lopez, Marco
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/180299
- Identifier
- vital:15723
- Identifier
-
https://doi.org/10.1007/s11228-021-00583-3
- Identifier
- ISBN:0927-6947 (ISSN)
- Abstract
- 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. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.
- Publisher
- Springer Science and Business Media B.V.
- Relation
- Set-Valued and Variational Analysis Vol. 29, no. 3 (2021), p. 683-699; 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 © 2021, The Author(s), under exclusive licence to Springer Nature B.V.
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Convex optimization; Normal cone; Optimality conditions; Subdifferentials; Supremum of convex functions
- Full Text
- Reviewed
- Funder
- 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.
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