Abstract

The purpose of this article is to study convergence analysis of quasi-variational inequalities using a projection-type method coupled with inertial extrapolation step. First, we give strong convergence analysis of the sequence of iterates generated by our proposed method to the unique solution of quasi-variational inequality under some mild assumptions. Later, we show that the sequence converges linearly to the unique solution in a special case of choice of parameters. Another contribution in this article is that the inertial factor in our proposed method is allowed to be equal to 1 unlike other previously proposed inertial projection-type method for solving quasi-variational inequalities in the literature where inertial factor is assumed to be bounded away from 1.

摘要

本文的目的是研究拟变分不等式的收敛性分析，使用投影型方法结合惯性外推步骤。首先，我们对我们提出的方法生成的迭代序列在一些温和假设下对拟变分不等式的唯一解进行了强收敛性分析。后来，我们证明了在参数选择的特殊情况下，序列线性收敛到唯一解。本文的另一个贡献是，我们提出的方法中的惯性因子被允许等于 1，这与文献中其他先前提出的用于求解拟变分不等式的惯性投影型方法不同，其中惯性因子被假定为远离 1 .