Systems of variational inequalities with hierarchical variational inequality constraints for Lipschitzian pseudocontractions
Lu-Chuan Ceng, Adrian Petruşel, Jen‐Chih Yao, Yonghong Yao · Fixed Point Theory · 2019
In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an accretive operator in a real Banach space.We propose an implicit composite extragradient-like method based on the Mann iteration method, the viscosity approximation method and the Korpelevich extragradient method.Convergence results for the proposed iteration method are also established under some suitable assumptions.