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# The Radius of Metric Subregularity

- 1.0517219 - ÚTIA 2021 RIV NL eng J - Journal Article
**Dontchev, A. L. - Gfrerer, H. - Kruger, A.Y. - Outrata, Jiří**

The Radius of Metric Subregularity.*Set-Valued and Variational Analysis*. Roč. 28, č. 3 (2020), s. 451-473. ISSN 1877-0533. E-ISSN 1877-0541**R&D Projects**: GA ČR GA17-04301S; GA ČR GA17-08182S**Institutional support**: RVO:67985556**Keywords**: Well-posedness * Metric subregularity * Generalized differentiation**Subject RIV**: BA - General Mathematics**OECD category**: Pure mathematics**Impact factor**: 1.783, year: 2020**Method of publishing**: Open access

http://library.utia.cas.cz/separaty/2019/MTR/outrata-0517219.pdf https://link.springer.com/article/10.1007/s11228-019-00523-2

There is a basic paradigm, called here the radius of well-posedness, which quantifies the “distance” from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.

**Permanent Link:**http://hdl.handle.net/11104/0302501

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