| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 83 | |
| Number of page(s) | 25 | |
| DOI | https://doi.org/10.1051/cocv/2024070 | |
| Published online | 25 October 2024 | |
A variational approach to stability relative to a set of single-valued and set-valued mappings
1
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
2
Dong Thap University, Cao Lanh City 870000, Dong Thap, Vietnam
3
Research Center for Interneural Computing, China Medical University, Taichung 40402, Taiwan
* Corresponding author: qxlxajh@163.com
Received:
20
January
2024
Accepted:
10
September
2024
Based on the limiting normal cone relative to a set, we present in this paper the novel versions of the limiting coderivative relative to a set and subdifferentials relative to a set of multifunctions and singleton mappings, respectively. In addition to giving the necessary and sufficient conditions for the Aubin property relative to a set of multifunctions, the limiting coderivative relative to a set also provides a coderivative criterion for the metric regularity relative to a set of multifunctions. Besides, our study establishes sudifferential characteristics of the metric regularity and the locally Lipschitz continuity relative to a set for single-valued mappings. In finite dimensional spaces, our results are more general than the previous results. Furthermore, we also give examples to illustrate our results.
Mathematics Subject Classification: 49J53 / 90C30 / 90C31
Key words: Aubin property relative to a set / coderivative relative to a set / metric regularity relative to a set / normal cone relative to a set / subdifferential relative to a set
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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