A novel method for hierarchical variational inequality with split common fixed point constraint

We address the strongly monotone variational inequality problem over the solution set of the split common fixed point problem with demimetric mappings in real Hilbert spaces. In order to solve this problem, we propose a new method that makes use of the inertial method with a correction term and a self-adaptive step size strategy. To demonstrate the effectiveness and performance of our proposed algorithm, we present two numerical examples, where one is related to the constrained convex minimization problem and the other is related to an application that performs binary classification based on support vector machines.