Enlargements of the moreau–rockafellar subdifferential
- Authors: Abbasi, Malek , Kruger, Alexander , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 29, no. 3 (2021), p. 701-719
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: This paper proposes three enlargements of the conventional Moreau–Rockafellar subdifferential: the sup-, sup
Gateaux differentiability revisited
- Authors: Abbasi, Malek , Kruger, Alexander , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Applied Mathematics and Optimization Vol. 84, no. 3 (2021), p. 3499-3516
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: 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.