Smooth approximations of nonsmooth convex functions

被引:0
作者
Polyakva, L. N. [1 ]
机构
[1] St Petersburg State Univ, 7-9 Univ Skaya Nab, St Petersburg 199034, Russia
来源
VESTNIK SANKT-PETERBURGSKOGO UNIVERSITETA SERIYA 10 PRIKLADNAYA MATEMATIKA INFORMATIKA PROTSESSY UPRAVLENIYA | 2022年 / 18卷 / 04期
关键词
set-valued mapping; semicontinuous mapping; conjugate function; Kuratowski converge; infimal convolution operation; smooth approximation; CONVERGENCE; SETS;
D O I
10.21638/11701/spbu10.2022.408
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For an arbitrary convex function, using the infimal convolution operation, a family of continuously differentiable convex functions approximating it is constructed. The constructed approximating family of smooth convex functions Kuratowski converges to the function under consideration. If the domain of the considered function is compact, then such smooth convex approximations are uniform in the Chebyshev metric. The approximation of a convex set by a family of smooth convex sets is also considered.
引用
收藏
页码:535 / 547
页数:13
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