A NOTE ON THE (ACCELERATED) PROXIMAL GRADIENT METHOD FOR COMPOSITE CONVEX OPTIMIZATION

被引：0

作者：

Li, Qingjing ^{[1
]}

Tan, Li ^{[1
]}

Guo, Ke ^{[2
]}

机构：

[1] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Peoples R China

[2] China West Normal Univ, Sch Math & Informat, Sichuan Coll & Univ Key Lab Optimizat Theory & AP, Nanchong 637002, Peoples R China

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2022年 / 23卷 / 12期

基金：

中国博士后科学基金;

关键词：

Acceleration; convex programming; proximal gradient; convergence rate; THRESHOLDING ALGORITHM; SHRINKAGE; SUM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The proximal gradient method and its accelerated versions are widely studied under different scenarios. In this paper, we focus on the composite convex optimization problem and propose a relax assumption to adapt the step size of the proximal gradient method and its accelerated version without explicitly knowing the Lipschitz constant of the gradient of the smooth function. Under the proposed relaxed rules, we prove the convergence of the sequence and O(1/k) convergence rate in terms of function values for the proximal gradient method and the O(1/k(2)) convergence rate in terms of function values for the accelerated proximal gradient method, respectively.

引用

页码：2847 / 2857

页数：11

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