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
Hlavní autori: Yao, Wenfang, Meng, Kaiwen, Li, Minghua, Yang, Xiaoqi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht Springer Netherlands 01.12.2023
Springer Nature B.V
Predmet:
Analysis
Applied mathematics
Calculus
Mathematics
Mathematics and Statistics
Optimization
Sum rules
Relative Lipschitz-like property
90C31
58C07
Calculus rules
49J53
Generalized Mordukhovich criterion
49K40
Projectional coderivative
ISSN:1877-0533, 1877-0541
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-023-00698-9