Work

A variational approach to stability relative to a set of single-valued and set-valued mappings

Year: 2024

Type: article

Abstract: 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.

Source: ESAIM Control Optimisation and Calculus of Variations

DOI: 10.1051/cocv/2024070

Authors: Vo Duc Thinh, Xiaolong Qin, Jen-Chih Yao

Institutions: Zhejiang Normal University, Dong Thap University, China Medical University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

OpenAlex ID: W4402543711