In this paper, we propose a new modified algorithm for finding an element of the set of solutions of a pseudomonotone, Lipschitz continuous variational inequality problem in real Hilbert spaces. Using the technique of double inertial steps into a single projection method we give weak and strong convergence theorems of the proposed algorithm. The weak convergence does not require prior knowledge of the Lipschitz constant of the variational inequality mapping and only computes one projection onto a feasible set per iteration as well as without using the sequentially weak continuity of the associated mapping. Under additional strong pseudomonotonicity and Lipschitz continuity assumptions, the R-linear convergence rate of the proposed algorithm is presented. Finally, some numerical examples are given to illustrate the effectiveness of the algorithms.

在本文中，我们提出了一种新的改进算法，用于寻找实希尔伯特空间中的伪单调、Lipschitz 连续变分不等式问题的解集的元素。使用双惯性步骤技术到单投影方法中，我们给出了所提出算法的弱收敛和强收敛定理。弱收敛不需要变分不等式映射的 Lipschitz 常数的先验知识，并且每次迭代仅计算到可行集的一个投影，并且不使用相关映射的顺序弱连续性。在额外的强伪单调性和 Lipschitz 连续性假设下，给出了该算法的R线性收敛速度。最后，给出了一些数值例子来说明算法的有效性。