On metric subregularity for set-valued mappings under additive perturbations

In this paper, we derive new sufficient conditions together with the moduli estimation for metric subregularity of sum mappings consisting of a set-valued mapping and a continuous but possibly nonsmooth single-valued additive part. The obtained results address subregularity simultaneously in three d...

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Vydané v:Applicable analysis Ročník 104; číslo 18; s. 3687 - 3716
Hlavní autori: Ouyang, Wei, Zhang, Binbin, Zhu, Jiangxing
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 12.12.2025
Taylor & Francis Ltd
Predmet:
Banach spaces
coderivative
error bound
Mapping
Metric subregularity/regularity
Perturbation
Stability
subdifferential
ISSN:0003-6811, 1563-504X
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Abstract In this paper, we derive new sufficient conditions together with the moduli estimation for metric subregularity of sum mappings consisting of a set-valued mapping and a continuous but possibly nonsmooth single-valued additive part. The obtained results address subregularity simultaneously in three different settings: general Banach spaces, Asplund spaces, and an Asplund pre-image space and a Banach image space with a norm which is Fréchet differentiable at nonzero points. We show that the stability of metric subregularity property under additive small perturbations by a smooth, or Lipschitz continuous, or specific type of nondifferentiable single-valued mapping, respectively, is equivalent. Finally, we establish some conditions for the stability of error bound property and metric regularity as applications.
AbstractList In this paper, we derive new sufficient conditions together with the moduli estimation for metric subregularity of sum mappings consisting of a set-valued mapping and a continuous but possibly nonsmooth single-valued additive part. The obtained results address subregularity simultaneously in three different settings: general Banach spaces, Asplund spaces, and an Asplund pre-image space and a Banach image space with a norm which is Fréchet differentiable at nonzero points. We show that the stability of metric subregularity property under additive small perturbations by a smooth, or Lipschitz continuous, or specific type of nondifferentiable single-valued mapping, respectively, is equivalent. Finally, we establish some conditions for the stability of error bound property and metric regularity as applications.
Author Zhang, Binbin
Ouyang, Wei
Zhu, Jiangxing
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  surname: Zhu
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  organization: Yunnan University
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Snippet In this paper, we derive new sufficient conditions together with the moduli estimation for metric subregularity of sum mappings consisting of a set-valued...
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SubjectTerms Banach spaces
coderivative
error bound
Mapping
Metric subregularity/regularity
Perturbation
Stability
subdifferential
Title On metric subregularity for set-valued mappings under additive perturbations
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