求解变分不等式与不动点问题公共解的新Tseng型外梯度算法

摘要/Abstract

摘要：

该文在Hilbert空间中提出一种新Tseng型外梯度算法, 用以求解一致连续伪单调映射的变分不等式问题与具有半封闭性拟非扩张映射的不动点问题的公共解. 在一定的假设条件下, 证明了算法所生成的序列的强收敛性. 文章最后对算法进行数值实验, 验证了算法的有效性.

关键词: 变分不等式, 不动点问题, 伪单调映射, 拟非扩张映射, 强收敛

Abstract:

In this paper, we introduce a new inertial Tseng-like extragradient algorithm for finding a common element of the set of solutions of a variational inequalitiy problem with a pseudomonotone and non-Lipschitz continuous mapping and the set of a fixed point problem with a quasi-nonexpansive mapping in Hilbert spaces. The strong convergence of the sequences generated by the algorithm is proved under some suitable assumptions imposed on the parameters. Finally, numercial experiments are carried out on the algorithm to verify the effectiveness of the algorithm.

Key words: Variational inequalitiy, Fixed point problem, Pseudomonotone mapping, Quasi-nonexpansive mapping, Strong convergence

中图分类号:

O244

段洁, 夏福全. 求解变分不等式与不动点问题公共解的新Tseng型外梯度算法[J]. 数学物理学报, 2023, 43(1): 274-290.

Duan Jie, Xia Fuquan. A New Tseng-like Extragradient Algorithm for Common Solutions of Variational Inequalities and Fixed Point Problems[J]. Acta mathematica scientia,Series A, 2023, 43(1): 274-290.

图/表 6

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例1 $\varepsilon=10^{-2}$ 时, 各算法的Iter与Time 结果比较"

表1

表2

例1 $\varepsilon=10^{-3}$ 时, 各算法的Iter与Time 结果比较"

表2

表3

例1 $\varepsilon=10^{-4}$ 时, 各算法的Iter与Time 结果比较"

表3

表4

例2 $\varepsilon=10^{-2}$ 时, 各算法的Iter与Time 结果比较"

表4

表5

例2 $\varepsilon=10^{-3}$ 时, 各算法的Iter与Time 结果比较"

表5

表6

例2 $\varepsilon=10^{-4}$ 时, 各算法的Iter与Time 结果比较"

表6

参考文献 23

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