About error bounds in metrizable topological vector spaces
- Authors: Abbasi, Malek , Théra, Michel
- Date: 2022
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1291-1311
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- Description: This paper aims to present some sufficient criteria under which a given function between two spaces that are either topological vector spaces whose topologies are generated by metrics or metrizable subsets of some topological vector spaces, satisfies the error bound property. Then, we discuss the Hoffman estimation and obtain 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 to calculate the coefficient of the error bound. The applications of this presentation are illustrated by some examples. © 2022, This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.
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.
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).