Geodesic
The Pli\'s 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. 
@article{SM_2019_210_7_a0,
     author = {M. V. Balashov},
     title = {The {Pli\'s} metric and {Lipschitz} stability of minimization problems},
     journal = {Sbornik. Mathematics},
     pages = {911--927},
     publisher = {mathdoc},
     volume = {210},
     number = {7},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_7_a0/}
}
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M. V. Balashov. The Pli\'s 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/