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Set-Valued and Variational Analysis
Article . 2024 . Peer-reviewed
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Article . 2023
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On New Generalized Differentials with Respect to a Set and Their Applications

On new generalized differentials with respect to a set and their applications
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 14 Aug 2024Embargo end date: 01 Jan 2023 English Publisher:Springer Science and Business Media LLCJournal:Set-Valued and Variational Analysis, volume 32 (issn: 1877-0533, eissn: 1877-0541, Copyright policy )
Authors: Xiaolong Qin; Vo Duc Thinh; Jen-Chih Yao;

doi: 10.1007/s11228-024-00729-z , 10.48550/arxiv.2307.15389

arXiv: 2307.15389

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

Abstract

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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Keywords

normal cone with respect to a set, optimality condition, subdifferential with respect to a set, Aubin property with respect to a set, Numerical Analysis (math.NA), coderivative with respect to a set, Nonlinear programming, Optimization and Control (math.OC), Sensitivity, stability, parametric optimization, FOS: Mathematics, 49J53, 90C30, 90C31, Mathematics - Numerical Analysis, Mathematics - Optimization and Control, Set-valued and variational analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Average
Green