The Radius of Metric Subregularity

0517219 - ÚTIA 2021 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA17-04301S; GA ČR GA17-08182S
Institucionální podpora: RVO:67985556
Klíčová slova: Well-posedness * Metric subregularity * Generalized differentiation
Obor OECD: Pure mathematics
Impakt faktor: 1.783, rok: 2020
Způsob publikování: 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.
Trvalý link: http://hdl.handle.net/11104/0302501