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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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 31; no. 4; p. 36
Main Authors: Yao, Wenfang, Meng, Kaiwen, Li, Minghua, Yang, Xiaoqi
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2023
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-023-00698-9