The Hybrid Steepest Descent Method with Implicit Double Midpoint for Solving Variational Inequality over Triple Hierarchical Problems

Abstract

Because of the importance of the variational inequality problem that related to many other problems in various branches of science and engineering, it becomes one of the most popular topics which many researchers pay deeply attention to study on the way to solve and the way to apply. In this research, we study the monotone variational inequality over triple hierarchical problem. We propose a new implicit algorithm to find the solution with the strong convergence theorem which is proved and applied to guarantee its solution under some weak assumptions. Our results enhance those of Xu et al., Ke and Ma, Dhakal and Wutiphol and many other authors.