- Title
- Gateaux differentiability revisited
- Creator
- Abbasi, Malek; Kruger, Alexander; Théra, Michel
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/179557
- Identifier
- vital:15606
- Identifier
-
https://doi.org/10.1007/s00245-021-09754-y
- Identifier
- ISBN:0095-4616 (ISSN)
- Abstract
- We revisit some basic concepts and ideas of the classical differential calculus and convex analysis extending them to a broader frame. We reformulate and generalize the notion of Gateaux differentiability and propose new notions of generalized derivative and generalized subdifferential in an arbitrary topological vector space. Meaningful examples preserving the key properties of the original notion of derivative are provided. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
- Publisher
- Springer
- Relation
- Applied Mathematics and Optimization Vol. 84, no. 3 (2021), p. 3499-3516; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021
- Rights
- Open Access
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Convex function; Directional derivative; Gateaux differentiability; Moreau–Rockafellar subdifferential
- Full Text
- Reviewed
- Funder
- The research was supported by the Australian Research Council, project DP160100854.
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