
Journal of Convex Analysis 27 (2020), No. 1, 103116 Copyright Heldermann Verlag 2020 Lipschitz Stability of Extremal Problems with a Strongly Convex Set Maxim V. Balashov V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow 117997, Russia balashov73@mail.ru We prove that in a real Hilbert space some extremal problems are Lipschitz stable with respect to the set in some special metric (Plis metric). We also consider the Lipschitz stability of such problems in the Hausdorff metric and characterize metrics on the space of closed bounded convex sets with uniformly continuous metric projection as function of the set. Keywords: Hilbert space, metric projection, summand of a convex set, Plis metric, Hausdorff metric, uniform continuity, integral of setvalued mapping. MSC: 49J53, 52A07, 46C05, 26B25; 46B25, 46B20. [ Fulltextpdf (126 KB)] for subscribers only. 