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

被引：6
|
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：
SET-VALUED AND VARIATIONAL ANALYSIS | 2021年 / 29卷 / 02期
基金：
俄罗斯科学基金会;
关键词：
Lipschitz continuous gradient; Proximal smoothness; Gradient projection algorithm; Metric projection; Nonconvex extremal problem; Lezanski-Polyak-Lojasiewicz condition; WEAK CONVEXITY;
D O I：
10.1007/s11228-020-00550-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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
收藏
页码：341 / 360
页数：20
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