Metric Regularity Relative to a Cone

Ngai, Huynh Van; Tron, Nguyen Huu; Théra, Michel

doi:10.1007/s10013-019-00361-7

Vietnam J. Math.

2019

DOI: 10.1007/s10013-019-00361-7

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Metric Regularity Relative to a Cone

Huynh Van Ngai

Nguyen Huu Tron

Michel Théra

Abstract: In this note, we introduce the concept of metric regularity with respect to a cone. A slope characterization of the relative metric regularity with respect to a cone, as well as a stability result is established. Then, some coderivative characterizations of metric regularity relative to a cone are given.

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Cited by 2 publications

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

Thinh,

Qin,

Yao

2024

ESAIM: COCV

View full text Add to dashboard Cite

show abstract

Nonlinear metric regularity on fixed sets

2022

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Metric Regularity Relative to a Cone

Cited by 2 publications

References 35 publications

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

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

Nonlinear metric regularity on fixed sets

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