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The Radius of Metric Subregularity

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    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

     
     
Number of the records: 1