A HYBRID STEEPEST DESCENT METHOD FOR BILEVEL VARIATIONAL INEQUALITY PROBLEMS WITH THE FIXED POINT SET

In this paper, we present a new hybrid steepest decent algorithm to solve the bilevel variational inequality problems, where the feasible set is the intersection of a variational inequality problem and the fixed point set of a nonexpansive mapping in a real Hilbert space. An iterative algorithm is introduced by using the hybrid steepest descent method and fixed-point formulation techniques. The strong convergence of the iterative sequences generated by the algorithm is shown under some suitable assumptions. In addition, the efficiency of our suggested algorithm is established by a numerical example.