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The Radius of Metric Subregularity
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SYSNO ASEP 0517219 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název The Radius of Metric Subregularity Tvůrce(i) Dontchev, A. L. (US)
Gfrerer, H. (AT)
Kruger, A.Y. (AU)
Outrata, Jiří (UTIA-B) RID, ORCIDCelkový počet autorů 4 Zdroj.dok. Set-Valued and Variational Analysis. - : Springer - ISSN 1877-0533
Roč. 28, č. 3 (2020), s. 451-473Poč.str. 23 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Well-posedness ; Metric subregularity ; Generalized differentiation Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA17-04301S GA ČR - Grantová agentura ČR GA17-08182S GA ČR - Grantová agentura ČR Způsob publikování Open access Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000554706900002 EID SCOPUS 85075389144 DOI 10.1007/s11228-019-00523-2 Anotace 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. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2021 Elektronická adresa https://link.springer.com/article/10.1007/s11228-019-00523-2
Počet záznamů: 1