The aim of this paper is to introduce a new inertial Tseng’s extragradient algorithm for solving variational inequality problems with pseudo-monotone and Lipschitz continuous mappings and fixed point problems for nonexpansive mappings in real Hilbert spaces. We prove a strong convergence theorem for the proposed algorithm under suitable assumptions imposed on the parameters. Finally, we give some numerical experiments for supporting our main results.

中文翻译：

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曾惯性的渐进梯度法求解变分不等式问题和不动点问题的强收敛定理。

本文的目的是介绍一种新的惯性曾氏超梯度算法，用于解决伪单调和Lipschitz连续映射的变分不等式问题以及实希尔伯特空间中非膨胀映射的不动点问题。我们在参数施加的适当假设下证明了所提出算法的强收敛定理。最后，我们给出一些数值实验来支持我们的主要结果。