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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

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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.

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Strongly regular points of mappings

Authors: Abbasi, Malek , Théra, Michel
Date: 2021
Type: Text , Journal article
Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (Journal article 2021), p.
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Description: In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound. © 2021, The Author(s).

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