Solving Bilevel quasimonotone variational inequality problem in Hilbert spaces

In this paper, we propose and study a Bilevel quasimonotone Variational Inequality Problem (BVIP) in the frame work of Hilbert space. We introduce a new modified inertial iterative technique with self-adaptive step size for approximating a solution of the BVIP. In addition, we established a strong convergence result of the proposed iterative technique with an adaptive step-size conditions without prior knowledge of Lipschitz’s constant of the cost operators as well as the strongly monotonicity coefficient under some standard mild assumptions. Finally, we provide some numerical experiments to demonstrate the efficiency of our proposed methods in comparison with some recently announced results in the literature.