摘要
本文在实Hilbert空间中提出了一种求解伪单调变分不等式问题的修正Tseng外梯度算法.该算法具有新的步长规则,即步长为自适应步长和Armijo型线搜索规则意义下的步长的最大值.在适当的条件下,我们证明了由该算法所产生的序列强收敛于伪单调变分不等式问题的解集和k-半压缩映射不动点集的公共元.最后,我们给出了一些数值实验来说明我们所提出算法的有效性与优越性.本文所得的结果推广和改进了文献中的一些已有结果.
In this paper,a modified Tseng's extragradient gradient algorithm for solving pseudo-monotone variational inequality problems in real Hilbert space is proposed.This algo-rithm has new step rules whose step length is the maximizer of the step length of a self-adaptive rule and that of an Armijo rule.Under appropriate conditions,we prove that the sequences generated by the algorithm strongly converge to a common element of the solution set of pseudo-monotone variational inequality problems and the fixed point set of k-demicontractive mappings.Finally,we give some numerical experiments to illustrate the effectiveness and superiority of our proposed algorithm.The results obtained in this paper generalize and improve some known results intheliterature.
作者
仇英茗
彭建文
QIU Yingming;PENG Jianwen(School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,P.R.China)
出处
《数学进展》
北大核心
2025年第4期891-911,共21页
Advances in Mathematics(China)
基金
国家自然科学基金面上项目(No.12271071)
国家自然科学基金重大项目(No.11991024)
重庆英才·创新创业领军人才·创新创业示范团队项目(No.CQYC20210309536)
重庆英才包干制项目(No.cstc2022ycjhbgzxm0147)
重庆市高校创新研究群体项目(No.CXQT20014)
重庆市自然科学基金项目(No.cstc2021jcyjmsxmX0300)。
关键词
伪单调算子
变分不等式
Tseng外梯度算法
强收敛
不动点
pseudomonotone operator
variational inequality
Tseng's extragradient algo-rithm
strong convergence
fixed point
