In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.

在本文中，我们提出了两种新的惯性投影型方法，用于解决有限维空间中的多值变分不等式问题。当与问题相关的多值映射只需要局部有界而没有任何单调性假设时，我们建立由这些方法生成的序列的收敛性。此外，我们在本文中采用的惯性技术与大多数论文中使用的惯性技术完全不同。此外，基于我们方法中惯性因子的较弱假设，我们得出了我们方法的几种特殊情况。最后，我们给出一些实验结果，以说明通过引入惯性外推步骤而获得的利润。