求解变分不等式和不动点问题的公共元的修正次梯度外梯度算法

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1517-1536.

求解变分不等式和不动点问题的公共元的修正次梯度外梯度算法

刘丽平(),彭建文*()

^{重庆师范大学数学科学学院重庆 401331}

收稿日期:2021-12-06 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 彭建文 E-mail:1318286263@qq.com;jwpeng6@aliyun.com
作者简介:刘丽平, E-mail: 1318286263@qq.com
基金资助:
国家自然科学基金面上项目(11171363);重庆英才·创新创业领军人才·创新创业示范团队项目(CQYC20210309536);重庆市高校创新研究群体项目(CXQT20014);重庆市自然科学基金项目(cstc 2021jcyj-msxmX0300)

Modified Subgradient Extragradient Algorithms for Solving Common Elements of Variational Inequality and Fixed Point Problems

Liping Liu(),Jianwen Peng*()

^{School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331}

Received:2021-12-06 Online:2022-10-26 Published:2022-09-30
Contact: Jianwen Peng E-mail:1318286263@qq.com;jwpeng6@aliyun.com
Supported by:
the National Natural Science Foundation of China(11171363);the Team Project of Innovation Leading Talent in Chongqing(CQYC20210309536);the Chongqing University Innovation Research Group Project(CXQT20014);the Basic and Advanced Research Project of Chongqing(cstc 2021jcyj-msxmX0300)

摘要/Abstract

摘要：

该文在实Hilbert空间中引入了一类新的求解变分不等式问题的惯性次梯度外梯度算法. 在适当的参数假设下, 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与拟非扩张映射不动点集合的公共元素. 最后, 给出了数值实验来说明所提算法的有效性. 该文所得的结果推广和改进了文献中的一些已有结果.

关键词: 变分不等式, 不动点, 伪单调, 次梯度外梯度算法

Abstract:

In this paper, we introduce a new class of inertial subgradient extragradient algorithms for solving variational inequality problems in the real Hilbert space. Under some appropriate conditions imposed on the parameters, we prove that the sequence generated by the algorithm strongly converges to a common element of the solution set for a pseudomonotone variational inequality problem and the set of fixed points for a quasinonexpansive mapping. Finally, we give numerical experiments to illustrate the effectiveness of our proposed algorithm. The results obtained in this paper extend and improve some existing results in the literature.

Key words: Variational inequality, Fixed point, Pseudomonotone, Subgradient extragradient method

中图分类号:

刘丽平,彭建文. 求解变分不等式和不动点问题的公共元的修正次梯度外梯度算法[J]. 数学物理学报, 2022, 42(5): 1517-1536.

Liping Liu,Jianwen Peng. Modified Subgradient Extragradient Algorithms for Solving Common Elements of Variational Inequality and Fixed Point Problems[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1517-1536.

图/表 4

参考文献 37

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