Strong convergence of extragradient methods for solving bilevel pseudo-monotone variational inequality problems

In this paper, we propose two extragradient methods for finding an element of the set of solutions of the bilevel pseudo-monotone variational inequality problems in real Hilbert spaces. The advantage of proposed algorithms requires only one projection onto the feasible set. The strong convergence theorems are proved under mild conditions. Our results improve related results in the literature. Finally, some numerical experiments are presented to show the efficiency and advantages of the proposed algorithms.