Directional Differentiability of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces

被引：0
作者：
Jinlu Li
机构：
[1] Shawnee State University,Department of Mathematics
来源：
Journal of Optimization Theory and Applications | 2024年 / 200卷
关键词：
Uniformly convex and uniformly smooth Banach space; Metric projection operator; Directional differentiability of the metric projection; Directional derivative of the metric projection; 49J50; 26A24; 47A58; 47J30; 49J40;
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摘要：
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. Let PC: X → C denote the (standard) metric projection operator. In this paper, we define the Ga^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document}teaux directional differentiability of PC. We investigate some properties of the Ga^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document}teaux directional differentiability of PC. In particular, if C is a closed ball or a closed and convex cone (including proper closed subspaces), then, we give the exact representations of the directional derivatives of PC.
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页码：923 / 950
页数：27
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