摘要
本文介绍了一种新的惯性Mann型算法,用于求解实Hilbert空间非扩张映射下的分裂变分包含问题和不动点问题.该算法的优点之一是不需要预先知道算子的范数.本文证明了参数和算子满足适当条件时,所给出的算法生成的迭代序列是强收敛的.最后,本文通过数值实验表明了该算法的有效性.
In this paper,we introduce a new inertial Mann-type algorithm for solving split variational inclusion problems and fixed point problems for a nonexpansive mapping in real Hilbert spaces.One of the advantages of the suggested algorithm is that it can work without knowing the prior information of the operator norm.Under some appropriate conditions imposed on the parameters and operators,we prove that the iterative sequence generated by our proposed algorithm is strongly convergent.Finally,some numerical experiments are given to illustrate the efficiency of our proposed algorithm.
作者
游利悦
蔡钢
董巧丽
YOU Liyue;CAI Gang;DONG Qiaoli(School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,P.R.China;College of Science,Civil Aviation University of China,Tianjin,300300,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第3期540-558,共19页
Advances in Mathematics（China）
基金
Supported by NSFC(No.12171062)
Natural Science Foundation of Chongqing Province(No.CSTB2022NSCQ-JQX0004)
Science and Technology Project of Chongqing Education Committee(No.KJZDK201900504)
Program of Chongqing Innovation Research Group Project in University(No.CXQT19018)
Graduate Research Innovation Project of Chongqing(Nos.CYS21269,CYS22553)
关键词
分裂变分包含问题
强收敛
惯性算法
Mann型算法
不动点
split variational inclusion problem
strong convergence
inertial method
Mann-type method
fixed point
