Thong et al. (A strong convergence theorem for Tseng's extragradient method for solving variational inequality problems. Optim Lett. 2020;14:1157–1175) introduced inertial Tseng's extragradient method to variational inequality problems for monotone and Lipschitz continuous mappings. In this work, we extend this method for solving variational inequality problems with pseudo-monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm provides the strong convergence without using the viscosity technique, as well as the monotonicity of the associated mapping. The advantage of the second algorithm is that it does not require the knowledge of the Lipschitz constants of the variational inequality mappings. Finally, some numerical experiments illustrating the performance of our algorithms are discussed.

丁字裤等人。（用于解决变分不等式问题的 Tseng 外梯度方法的强收敛定理。Optim Lett. 2020;14:1157–1175）将惯性 Tseng 外梯度方法引入了单调和 Lipschitz 连续映射的变分不等式问题。在这项工作中，我们扩展了这种方法来解决伪单调的变分不等式问题和实希尔伯特空间中的 Lipschitz 连续映射。第一种算法在不使用粘性技术的情况下提供了强收敛性，以及相关映射的单调性。第二种算法的优点是它不需要知道变分不等式映射的 Lipschitz 常数。最后，讨论了一些说明我们算法性能的数值实验。