Iterative methods for solving variational inequality problems with a double-hierarchical structure in Hilbert spaces

This paper deals with a variational inequality problem over a solution set of another variational inequality problem, which essentially is called the double-hierarchical constrained optimization problem. Inertial-based algorithms are devised for this problem and solution theorems of strong convergence are established. Simulation results on numerical examples are given to illustrate the behaviour of our proposed algorithms compared with some existing ones.