Geodesic
The Pliś metric and Lipschitz stability of minimization problems
Sbornik. Mathematics, Tome 210 (2019) no. 7, pp. 911-927

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
M. V. Balashov. The Pliś metric and Lipschitz stability of minimization problems. Sbornik. Mathematics, Tome 210 (2019) no. 7, pp. 911-927. http://geodesic.mathdoc.fr/item/SM_2019_210_7_a0/
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     title = {The {Pli\'s} metric and {Lipschitz} stability of minimization problems},
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