The Radius of Metric Subregularity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00517219" target="_blank" >RIV/67985556:_____/20:00517219 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11228-019-00523-2" target="_blank" >https://link.springer.com/article/10.1007/s11228-019-00523-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11228-019-00523-2" target="_blank" >10.1007/s11228-019-00523-2</a>
Alternative languages
Result language
angličtina
Original language name
The Radius of Metric Subregularity
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Set-Valued and Variational Analysis
ISSN
1877-0533
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
23
Pages from-to
451-473
UT code for WoS article
000554706900002
EID of the result in the Scopus database
2-s2.0-85075389144