Lipschitz Continuity of the Optimal Solution of the Infimal Convolution Problem and Subdifferential Calculus

被引：0

作者：

Ivanov, Grigorii E. ^{[1
]}

Golubev, Maxim O. ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, 9 Inst Skiy Per, Dolgoprudnyi 141700, Moscow Region, Russia

来源：

OPTIMIZATION AND APPLICATIONS, OPTIMA 2019 | 2020年 / 1145卷

基金：

俄罗斯基础研究基金会;

关键词：

Parametrized optimization problem; Infimal convolution; Best approximation problem; Marginal function; Tykhonov well-posedness; Frechet subdifferential; Limiting subdifferential; WEAK CONVEXITY; SETS;

D O I：

10.1007/978-3-030-38603-0_6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider a parametrized constrained optimization problem, which can be represented as the Moreau-type infimal convolution of the norm and some (nonconvex in general) function f. This problem arises particularly in optimal control and approximation theory. We assume that the admissible set A is weakly convex and function f is Lipschitz continuous and weakly convex on the convex hull of A. We show that the problem is Tykhonov well-posed and the solution of the problem is unique and Lipschitz continuous in some neighbourhood of A. Exact estimates for the size of the neighbourhood and for the Lipschitz constant are obtained. Based on these results we prove lower regularity of the optimal value (marginal) function of this problem in some neighbourhood of A.

引用

页码：72 / 87

页数：16

共 19 条

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