Abstract
This paper is devoted to the study of a newly introduced tool, projectional coderivatives, and the corresponding calculus rules in finite dimensional spaces. We show that when the restricted set has some nice properties, more specifically, it is a smooth manifold, the projectional coderivative can be refined as a fixed-point expression. We will also improve the generalized Mordukhovich criterion to give a complete characterization of the relative Lipschitz-like property under such a setting. Chain rules and sum rules are obtained to facilitate the application of the tool to a wider range of parametric problems.
| Original language | English |
|---|---|
| Article number | 36 |
| Number of pages | 27 |
| Journal | Set-Valued and Variational Analysis |
| Volume | 31 |
| Issue number | 4 |
| Early online date | 30 Oct 2023 |
| DOIs | |
| Publication status | Published - Dec 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive licence to Springer Nature B.V.
Funding
Kaiwen Meng was supported in part by the National Natural Science Foundation of China (Ref No.: 11671329, 12001445). Minghua Li was supported by the National Natural Science Foundation of China (Ref No.: 12271072) and the Natural Science Foundation of Chongqing Municipal Science and Technology Commission (Ref No.: CSTB2022NSCQ-MSX0409, CSTB2022NSCQ-MSX0406). Yang Xiaoqi was partly supported by a project from the Research Grants Council of Hong Kong (Ref No.: 15209921).
Keywords
- Calculus rules
- Generalized Mordukhovich criterion
- Projectional coderivative
- Relative Lipschitz-like property