We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.

我们考虑希尔伯特空间中的单调变分不等式问题，并描述一种具有以下性质的带有惯性项的投影型方法：（a）该方法生成一个强收敛的迭代序列；（b）该方法每次迭代都只需要对可行集进行一次投影，并对操作员进行两次评估；（c）该方法设计用于变分不等式，对于该不等式，下划线算子是单调且一致连续的；（d）该方法包括惯性项。后者也被证明可以加快我们数值结果的收敛速度。通过与一些相关方法的比较，表明该新方法很有希望。