- Title
- Valadier-like formulas for the supremum function I
- Creator
- Correa, Rafael; Hantoute, Abderrahim; López, Marco
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/165957
- Identifier
- vital:13363
- Identifier
- ISBN:0944-6532
- Abstract
- We generalize and improve the original characterization given by Valadier [19, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdifferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to the Valadier formula. Our starting result is the characterization given in [11, Theorem 4], which uses the e-subdifferential at the reference point.
- Publisher
- Heldermann Verlag
- Relation
- Journal of Convex Analysis Vol. 25, no. 4 (2018), p. 1253-1278; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright © 2018 Heldermann Verlag. All rights reserved.
- Rights
- This metadata is freely available under a CCO license
- Rights
- Open Access
- Subject
- 0101 Pure Mathematics; Convex functions; Fenchel subdifferential; Pointwise supremum function; Valadier-like formulas
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