- Title
- A new tour on the subdifferential of the Supremum function
- Creator
- Hantoute, Abderrahim; López-Cerdá, Marco
- Date
- 2023
- Type
- Text; Conference paper
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/195899
- Identifier
- vital:18596
- Identifier
-
https://doi.org/10.1007/978-3-031-30014-1_8
- Identifier
- ISBN:2194-1009 (ISSN); 9783031300134 (ISBN)
- Abstract
- This chapter is a survey presenting various characterizations of the subdifferential of the pointwise supremum of convex functions, as well as some featured applications. We gathered here the main outcomes we obtained in a series of recent papers, dealing with different models, assumptions and scenarios. Starting by the maximum generality framework, we move after to particular contexts in which some continuity and compactness assumptions are either imposed or inforced via processes of compactification of the index set and regularization of the data functions. Some relevant applications of the general results are presented, in particular to derive rules for the subdifferential of the sum, and for convexifying a general (unconstrained) optimization problem. The last section gives some specific constraint qualifications for the convex optimization problem with an arbitrary set of constraints, and also contains different sets of KKT-type optimality conditions appealing to the subdifferential of the supremum function. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
- Publisher
- Springer
- Relation
- International Meeting on Functional Analysis and Continuous Optimization, IMFACO 2022, Elche, Spain, 16-17 June 2022, Functional Analysis and Continuous Optimization In Honour of Juan Carlos Ferrando's 65th Birthday, Elche, Spain, June 16–17, 2022 Vol. 424, p. 167-194
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2023, The Author(s)
- Subject
- Convex optimization; KKT-optimality conditions; Subdifferential calculus rules; Supremum of convex functions
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