This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each iteration, the proposed method is updated based on the ideas of a hybrid conjugate gradient method used to accelerate the well-known hybrid steepest descent method, and an extrapolated cyclic cutter method for solving a common fixed-point problem. We prove strong convergence of the method under some suitable assumptions of step-size sequences. We finally show the numerical efficiency of the proposed method compared to some existing methods.

本文讨论了变分不等式问题的解决，其中将约束集作为多个不动点集的交集给出。为此，我们提出了一种外推的顺序约束方法。在每次迭代中，基于用于加速众所周知的混合最速下降法的混合共轭梯度法和用于解决常见定点问题的外推循环刀具法的思想，对所提出的方法进行了更新。我们在步长序列的一些适当假设下证明了该方法的强收敛性。最后，我们证明了与现有方法相比，该方法的数值效率。