Projectional Coderivatives and Calculus Rules
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 b...
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| Vydané v: | Set-valued and variational analysis Ročník 31; číslo 4; s. 36 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Dordrecht
Springer Netherlands
01.12.2023
Springer Nature B.V |
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| ISSN: | 1877-0533, 1877-0541 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 36 |
| Author | Yang, Xiaoqi Yao, Wenfang Meng, Kaiwen Li, Minghua |
| Author_xml | – sequence: 1 givenname: Wenfang orcidid: 0000-0002-6835-5030 surname: Yao fullname: Yao, Wenfang email: dorothy.wf.yao@connect.polyu.hk organization: Department of Applied Mathematics, The Hong Kong Polytechnic University – sequence: 2 givenname: Kaiwen surname: Meng fullname: Meng, Kaiwen organization: School of Mathematics and Fintech Innovation Center, Southwestern University of Finance and Economics – sequence: 3 givenname: Minghua surname: Li fullname: Li, Minghua organization: School of Mathematics and Big Data, Chongqing University of Arts and Sciences – sequence: 4 givenname: Xiaoqi surname: Yang fullname: Yang, Xiaoqi organization: Department of Applied Mathematics, The Hong Kong Polytechnic University |
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| Cites_doi | 10.1287/moor.1060.0203 10.1007/s10107-020-01568-0 10.1137/15M1052299 10.1137/1.9781611971309 10.1007/s11784-010-0021-0 10.1007/3-540-31246-3 10.1006/jmaa.1994.1144 10.1007/978-0-387-87821-8 10.1155/S0161171204405183 10.1007/978-3-319-92775-6 10.1287/moor.9.1.87 10.1137/22M151296X 10.1137/140998469 10.1137/110820981 10.1287/moor.2014.0705 10.1007/978-3-319-64277-2 10.1007/s11228-019-00516-1 10.1007/s11228-012-0220-5 10.1112/jlms/jdq084 10.1137/060665609 10.1007/s10107-003-0452-0 |
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| Keywords | Relative Lipschitz-like property 90C31 58C07 Calculus rules 49J53 Generalized Mordukhovich criterion 49K40 Projectional coderivative |
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