An inertial method for solving bilevel variational inequality problems with fixed point constraints

Abstract

In this paper, we introduce and study an inertial algorithm for solving bilevel variational inequality problems with a fixed point constraint involving a uniformly continuous pseudomonotone mapping in the lower level variational inequality problem and a demimetric mapping for the fixed point constraint. We prove a strong convergence theorem under some suitable conditions on the control sequences. We also provide a numerical example to demonstrate the effectiveness of the method.