Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems

Abstract

In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.