一类新的伪单调惯性次梯度外梯度粘性方法

A New Kind of Inertial Subgradient Extragradient Methods for Solving Pseudomonotone Variational Inequalities

本文考虑希尔伯特空间上的伪单调变分不等式的求解算法。在现有文献的基础上,通过引入自适应步长规则和结合粘性逼近法,给出了一个新的求解伪单调变分不等式问题的惯性次梯度外梯度方法,并在一般假设条件成立下,证明了新算法在希尔伯特空间中具有强收敛性。与现有文献相比,新算法的收敛条件减弱,并且新算法的收敛性更强。

In this paper, we consider an algorithm for solving pseudomonotone variational inequalities in Hilbert Spaces. Based on the existing literature, a new Inertial Subgradient Extragradient method for solving pseudomonotone variational inequalities is presented by introducing adaptive step rule and viscous approximation method. And under the general assumptions, it is proved that the new algorithm has strong convergence in Hilbert space. Compared with the existing literature, the convergence condition of the new algorithm is weakened, and the convergence of the new algorithm is stronger.