An inertial projection and contraction method for solving bilevel quasimonotone variational inequality problems

In this paper, we study an iterative algorithm that is based on inertial projection and contraction methods for solving bilevel quasimonotone variational inequality problems in the framework of real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on adaptive stepsizes conditions without prior knowledge of Lipschitz constant of the cost operator as well as the strongly monotonicity coefficient under some standard mild assumptions on the algorithm parameters. Finally, we present some special numerical experiments to show efficiency and comparative advantage of our algorithm to other related methods in the literature. The results presented in this article improve and generalize some well-known results in the literature.