Email this article The Plis metric and Lipschitz stability of minimization problems
- Authors: Balashov M.V.1
-
Affiliations:
- V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
- Issue: Vol 210, No 7 (2019)
- Pages: 3-20
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/142378
- DOI: https://doi.org/10.4213/sm9128
- ID: 142378
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Abstract
We study the metric introduced by Plis 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 Plis 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.
About the authors
Maxim Viktorovich Balashov
V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Email: balashov73@mail.ru
Doctor of physico-mathematical sciences, Associate professor
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