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

Abstract

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

CLC Number:

O244

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.

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A New Tseng-like Extragradient Algorithm for Common Solutions of Variational Inequalities and Fixed Point Problems

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