On New Generalized Differentials with Respect to a Set and Their Applications

The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, b...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 32; no. 3; p. 27
Main Authors: Qin, Xiaolong, Duc Thinh, Vo, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.09.2024
Springer Nature B.V
Subjects:
Analysis
Cones
Constraining
Euclidean space
Mathematics
Mathematics and Statistics
Optimality criteria
Optimization
90C31
Subdifferential with respect to a set
90C30
Aubin property with respect to a set
49J53
Coderivative with respect to a set
Optimality condition
Normal cone with respect to a set
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes.
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-024-00729-z