The article introduces a new algorithm for solving a class of variational inequality problems for monotone operators and system of nonlinear variational inequalities problems for two inverse strongly monotone operators. We describe how to incorporate the extragradient like technique based on altering points technique with inertial effects. A weak convergence theorem is established for the proposed algorithm. Numerical examples are performed to illustrate the numerical efficiency of the algorithm and compare with other algorithms.

中文翻译：

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变分不等式和变分不等式系统的惯性迭代算法

本文介绍了一种新的算法，用于解决一类单调算子的变分不等式问题和两个逆强单调算子的非线性变分不等式的系统。我们描述了如何结合具有惯性效应的基于变点技术的超梯度技术。针对该算法建立了一个弱收敛定理。数值例子说明了该算法的数值效率，并与其他算法进行了比较。