杭州师范大学学报（自然科学版）2025，Vol.24Issue(6)：657-663,7.DOI:10.19926/j.cnki.issn.1674-232X.2024.02.291
多目标Proximal-Gradient算法的收敛性分析
Convergence Analysis of the Multi-objective Proximal-Gradient Algorithm
摘要
Abstract
To investigate the convergence of the Proximal-Gradient algorithm for solving unconstrained multi-objective optimization problems,this study extends the classical Polyak-Lojasiewicz inequality(P-L inequality),the proximal P-L inequality,and the multi-objective proximal P-L inequality.A multi-objective generalized proximal P-L inequality with an exponent is introduced.Under the conditions that the differentiable part of the objective function satisfies the Lipschitz continuity of the gradient and the multi-objective generalized P-L inequality holds,convergence results of the Proximal-Gradient algorithm are derived.Furthermore,when the exponent is set to 1,linear convergence of the Proximal-Gradient algorithm is achieved.关键词
多目标优化/Proximal-Gradient算法/收敛速率/线性收敛Key words
multi-objective optimization/Proximal-Gradient algorithm/convergence rate/linear convergence分类
数理科学引用本文复制引用
张世豪,张露方,李尹..多目标Proximal-Gradient算法的收敛性分析[J].杭州师范大学学报（自然科学版）,2025,24(6):657-663,7.基金项目
浙江省自然科学基金项目(LQ24A010023) （LQ24A010023）
浙江科技大学青年科学基金项目(2023QN055). （2023QN055）
