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The Radius of Metric Subregularity
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SYSNO ASEP 0517219 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Radius of Metric Subregularity Author(s) Dontchev, A. L. (US)
Gfrerer, H. (AT)
Kruger, A.Y. (AU)
Outrata, Jiří (UTIA-B) RID, ORCIDNumber of authors 4 Source Title Set-Valued and Variational Analysis. - : Springer - ISSN 1877-0533
Roč. 28, č. 3 (2020), s. 451-473Number of pages 23 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords Well-posedness ; Metric subregularity ; Generalized differentiation Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA17-04301S GA ČR - Czech Science Foundation (CSF) GA17-08182S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UTIA-B - RVO:67985556 UT WOS 000554706900002 EID SCOPUS 85075389144 DOI 10.1007/s11228-019-00523-2 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2021 Electronic address https://link.springer.com/article/10.1007/s11228-019-00523-2
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