A projection and contraction method with adaptive step sizes for solving bilevel pseudo-monotone variational inequality problems

Abstract

In this paper, we propose a single projection method for finding a solution of the bilevel pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm requires only one projection onto the feasible set. Also, we prove strong convergence theorems of the proposed method under mild conditions, which improve some related results in the literature. Finally, we present some numerical experiments to show the efficiency and advantages of the proposed algorithm.