The Pliś metric and Lipschitz stability of minimization problems

M. V. Balashov

Sbornik. Mathematics, Tome 210 (2019) no. 7, pp. 911-927

Résumé

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.

Détail

Keywords: Pliś metric, Hausdorff metric, support function, strong convexity, Lipschitz continuous gradient.

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