Projectional Coderivatives and Calculus Rules
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914984691236864 |
|---|---|
| author | Yao, Wenfang Meng, Kaiwen Li, Minghua Yang, Xiaoqi |
| author_facet | Yao, Wenfang Meng, Kaiwen Li, Minghua Yang, Xiaoqi |
| contents | This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, 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 problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11706 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Projectional Coderivatives and Calculus Rules Yao, Wenfang Meng, Kaiwen Li, Minghua Yang, Xiaoqi Optimization and Control 49J53, 49K40, 58C07, 90C31 This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, 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 problems. |
| title | Projectional Coderivatives and Calculus Rules |
| topic | Optimization and Control 49J53, 49K40, 58C07, 90C31 |
| url | https://arxiv.org/abs/2210.11706 |