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Sbornik: Mathematics, 2019, Volume 210, Issue 7, Pages 911–927
DOI: https://doi.org/10.1070/SM9128 (Mi sm9128) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Pliś metric and Lipschitz stability of minimization problems

M. V. Balashov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
English version PDF (486 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM9128
Abstract: We study the metric introduced by Pliś on the set of convex closed bounded subsets of a Banach space. For a real Hilbert space it is proved that metric projection and (under certain conditions) metric antiprojection from a point onto a set satisfy a Lipschitz condition with respect to the set in the Pliś metric. It is proved that solutions of a broad class of minimization problems are also Lipschitz stable with respect to the set. Several examples are discussed.
Bibliography: 18 titles.
Keywords: Pliś metric, Hausdorff metric, support function, strong convexity, Lipschitz continuous gradient.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00259-а
18-01-00209-а
This work was supported by the Russian Foundation for Basic Research (grant nos. 16-01-00259-a and 18-01-00209-a).
Received: 23.04.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 7, Pages 3–20
DOI: https://doi.org/10.4213/sm9128
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: Primary 49J53, 52A20; Secondary 90C26
Language: English
Original paper language: Russian
Citation: M. V. Balashov, “The Pliś metric and Lipschitz stability of minimization problems”, Mat. Sb., 210:7 (2019), 3–20; Sb. Math., 210:7 (2019), 911–927
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:36
    First page:25
     
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