Projectional Coderivatives and Calculus Rules

Yao, Wenfang; Meng, Kaiwen; Li, Minghua; Yang, Xiaoqi

doi:10.1007/s11228-023-00698-9

Set-Valued Var. Anal

2023

DOI: 10.1007/s11228-023-00698-9

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Projectional Coderivatives and Calculus Rules

Wenfang Yao,

Kaiwen Meng,

Minghua Li

et al.

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2024

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Cited by 4 publications

References 21 publications

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Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications

Thinh,

Qin,

Yao

2024

J Optim Theory Appl

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Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications

Thinh,

Qin,

Yao

2024

J Optim Theory Appl

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

Qin,

Duc Thinh,

Yao

2024

Set-Valued Var. Anal

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A variational approach to stability relative to a set of single-valued and set-valued mappings

Thinh,

Qin,

Yao

2024

ESAIM: COCV

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Based on the limiting normal cone relative to a set, we present in this paper the novel versions of the limiting coderivative relative to a set and subdifferentials relative to a set of multifunctions and singleton mappings, respectively. In addition to giving the necessary and sufficient conditions for the Aubin property relative to a set of multifunctions, the limiting coderivative relative to a set also provides a coderivative criterion for the metric regularity relative to a set of multifunctions. Besides, our study establishes sudifferential characteristics of the metric regularity and the locally Lipschitz continuity relative to a set for single-valued mappings. In finite dimensional spaces, our results are more general than the previous results. Furthermore, we also give examples to illustrate our results.

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Projectional Coderivatives and Calculus Rules

Cited by 4 publications

References 21 publications

Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications

Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications

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

A variational approach to stability relative to a set of single-valued and set-valued mappings

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