- Title
- Variational analysis of paraconvex multifunctions
- Creator
- Van Ngai, Huynh; Tron, Nguyen; Van Vu, Nguyen; Théra, Michel
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185174
- Identifier
- vital:16646
- Identifier
-
https://doi.org/10.1007/s10957-022-02021-2
- Identifier
- ISBN:0022-3239 (ISSN)
- Abstract
- Our aim in this article is to study the class of so-called ρ- paraconvex multifunctions from a Banach space X into the subsets of another Banach space Y. These multifunctions are defined in relation with a modulus function ρ: X→ [0 , + ∞) satisfying some suitable conditions. This class of multifunctions generalizes the class of γ- paraconvex multifunctions with γ> 1 introduced and studied by Rolewicz, in the eighties and subsequently studied by A. Jourani and some others authors. We establish some regular properties of graphical tangent and normal cones to paraconvex multifunctions between Banach spaces as well as a sum rule for coderivatives for such class of multifunctions. The use of subdifferential properties of the lower semicontinuous envelope function of the distance function associated to a multifunction established in the present paper plays a key role in this study. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Publisher
- Springer
- Relation
- Journal of Optimization Theory and Applications Vol. 193, no. 1-3 (2022), p. 180-218; https://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
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; Approximate convex function; Coderivatives; Fréchet normal cone; Fréchet subdifferential; Fuzzy mean value theorem; Lower C2 functions; Paraconvexity; Paramonotonicity; Weak convexity
- Full Text
- Reviewed
- Funder
- Research of the Huynh Van Ngai was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.12 Research of the Michel Théra was supported by the Australian Research Council (ARC) Grant DP160100854 and benefited from the support of the FMJH Program PGMO and from the support of EDF.
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