Weak and strong convergence of generalized proximal point algorithms with relaxed parameters

被引：0
作者：
Hui Ouyang
机构：
[1] University of British Columbia,Mathematics
来源：
Journal of Global Optimization | 2023年 / 85卷
关键词：
Proximal point algorithm; Maximally monotone operators; Resolvent; Firmly nonexpansiveness; Weak convergence; Strong convergence; Primary 65J15; 47J25; 47H05; Secondary 90C25; 90C30;
D O I：
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学科分类号：
摘要：
In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal point algorithms for the equivalence of the boundedness of the sequence of iterations generated by this algorithm and the non-emptiness of the zero set of the maximally monotone operator, and for the weak and strong convergence of the algorithm. Our results cover or improve many results on generalized proximal point algorithms in our references. Improvements of our results are illustrated by comparing our results with related known ones.
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页码：969 / 1002
页数：33
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