Lipschitz Stability of Extremal Problems with a Strongly Convex Set

被引：0
|
作者：
Balashov, Maxim, V [1 ]
机构：
[1] Russian Acad Sci, VA Trapeznikov Inst Control Sci, 65 Profsoyuznaya St, Moscow 117997, Russia
来源：
JOURNAL OF CONVEX ANALYSIS | 2020年 / 27卷 / 01期
关键词：
Hilbert space; metric projection; summand of a convex set; Plis metric; Hausdorff metric; uniform continuity; integral of set-valued mapping; WEAK CONVEXITY;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：103 / 116
页数：14
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