广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (1): 128-138.doi: 10.16088/j.issn.1001-6600.2023032404

• 研究论文 • 上一篇    下一篇

伪单调变分不等式解集与拟非扩张映射不动点集公共元的强收敛定理

王永杰, 高兴慧*, 房萌凯   

  1. 延安大学 数学与计算机科学学院,陕西 延安 716000
  • 收稿日期:2023-03-24 修回日期:2023-06-02 出版日期:2024-01-25 发布日期:2024-01-19
  • 通讯作者: 高兴慧(1975—),女,陕西横山人,延安大学教授。E-mail:yadxgaoxinghui@163.com
  • 基金资助:
    国家自然科学基金(61866038);国家级大学生创新训练计划项目(202210719022)

Strong Convergence Theorem for Pseudomonotonic Variational Inequality Solution Sets and Quasi-non-expansionary Mapping Fixed Point Sets Common Elements

WANG Yongjie, GAO Xinghui*, FANG Mengkai   

  1. School of Mathematics and Computer Science, Yan’an University, Yan’an Shaanxi 716000, China
  • Received:2023-03-24 Revised:2023-06-02 Online:2024-01-25 Published:2024-01-19

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摘要： 在Hilbert空间中提出一种新的关于求解伪单调变分不等式问题的Tseng外梯度算法。在适当条件下,证明由此算法生成的迭代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的公共元,并用数值实验说明所提算法的有效性。

关键词: Hilbert空间, 变分不等式, 伪单调, 次梯度外梯度算法, 强收敛

Abstract: A new Tseng outer gradient algorithm for solving pseudomonotonic variational inequality problems is proposed in Hilbert space. Under appropriate conditions, it is proved that the iterative sequence generated by the algorithm strongly converges to the common element of the solution set of pseudomonotonic variational inequality problem and the set of fixed points of the quasi-non-expansion map, and numerical experiments are given to illustrate the effectiveness of the proposed algorithm.

Key words: Hilbert space, variational inequality, pseudo-monotony, subgradient external gradient algorithm, strong convergence

中图分类号:  O177.91

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