In this paper, we propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. We prove a strong convergence theorem under some appropriate conditions imposed on the parameters. Finally, we give some numerical experiments to illustrate the advantages of our proposed algorithms. The main results obtained in this paper extend and improve some related works in the literature.

中文翻译：

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用伪单调和非Lipschitz算子求解变分不等式问题的强收敛定理

在本文中，我们提出了一种新的粘度超梯度算法，用于解决实 Hilbert 空间中伪单调和非 Lipschitz 连续算子的变分不等式问题。我们证明了在对参数施加一些适当条件下的强收敛定理。最后，我们给出了一些数值实验来说明我们提出的算法的优点。本文获得的主要结果对文献中的一些相关工作进行了扩展和改进。