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Journal of Convex Analysis 27 (2020), No. 1, 103--116
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

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 set-valued mapping.

MSC: 49J53, 52A07, 46C05, 26B25; 46B25, 46B20.

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