Geodesic
Lipschitz Stability of Extremal Problems with a Strongly Convex Set
Journal of convex analysis, Tome 27 (2020) no. 1, pp. 103-116
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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.
Classification : 49J53, 52A07, 46C05, 26B25, 46B25, 46B20
Mots-clés : Hilbert space, metric projection, summand of a convex set, Plis metric, Hausdorff metric, uniform continuity, integral of set-valued mapping 
@article{JCA_2020_27_1_JCA_2020_27_1_a7,
     author = {M. V. Balashov},
     title = {Lipschitz {Stability} of {Extremal} {Problems} with a {Strongly} {Convex} {Set}},
     journal = {Journal of convex analysis},
     pages = {103--116},
     year = {2020},
     volume = {27},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_1_JCA_2020_27_1_a7/}
}
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M. V. Balashov. Lipschitz Stability of Extremal Problems with a Strongly Convex Set. Journal of convex analysis, Tome 27 (2020) no. 1, pp. 103-116. http://geodesic.mathdoc.fr/item/JCA_2020_27_1_JCA_2020_27_1_a7/