- Title
- Towards supremum-sum subdifferential calculus free of qualification conditions
- Creator
- Correa, Rafael; Hantoute, Abderrahim; López, Marco
- Date
- 2016
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154567
- Identifier
- vital:11114
- Identifier
-
https://doi.org/10.1137/15m1045375
- Identifier
- ISSN:1052-6234
- Abstract
- We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption expressing a natural relationship between the lower semicontinuous envelopes of the data functions in the domain of the sum function. We also provide a new rule for the subdifferential of the sum of two convex functions, which uses a strategy of augmenting the involved functions. The main feature of our analysis is that no continuity-type condition is required. Our approach allows us to unify, recover, and extend different results in the recent literature.
- Publisher
- SIAM Publications
- Relation
- Siam Journal on Optimization Vol. 26, no. 4 (2016), p. 2219-2234; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright © 2016 Society for Industrial and Applied Mathematics.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Sum and pointwise supremum of convex functions; Fenchel and approximate subdifferentials
- Full Text
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