In this work, we propose a new modified Popov’s method by using inertial effect for solving the variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration as well as it does not need to the prior knowledge of the Lipschitz constants of the variational inequality mapping. We present weak convergence theorem of the proposed algorithm under pseudomonotonicity and Lipschitz continuity of the associated mapping. Our results generalize and extend some related results in the literature and primary numerical experiments demonstrate the applicability of the scheme.

在这项工作中，我们提出了一种新的改进的Popov方法，该方法利用惯性效应解决了实际希尔伯特空间中的变分不等式问题。所提出的算法的优点在于，每次迭代仅计算不等式映射的一个值和在可允许集合上的一个投影，并且不需要变分不等式映射的Lipschitz常数的先验知识。我们在拟单调性和关联映射的Lipschitz连续性下给出了所提出算法的弱收敛定理。我们的研究结果概括并扩展了文献中的一些相关结果，主要的数值实验证明了该方案的适用性。