The Gradient Projection Algorithm for Smooth Sets and Functions in Nonconvex Case

被引：0

作者：

Maxim V. Balashov

机构：

[1] V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences,

来源：

Set-Valued and Variational Analysis | 2021年 / 29卷

关键词：

Lipschitz continuous gradient; Proximal smoothness; Gradient projection algorithm; Metric projection; Nonconvex extremal problem; Lezanski-Polyak-Lojasiewicz condition; Primary: 90C26; 65K05. Secondary: 46N10; 65K10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider the problem of minimization for a function with Lipschitz continuous gradient on a proximally smooth and smooth manifold in a finite dimensional Euclidean space. We consider the Lezanski-Polyak-Lojasiewicz (LPL) conditions in this problem of constrained optimization. We prove that the gradient projection algorithm for the problem converges with a linear rate when the LPL condition holds.

引用

页码：341 / 360

页数：19

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