A hybrid extragradient method for bilevel pseudomonotone variational inequalities with multiple solutions

In this paper, we introduce and analyze a hybrid extragradient algorithm for solving bilevel pseudomono-tone variational inequalities with multiple solutions in a real Hilbert space. The proposed algorithm is based on Korpelevich’s extragradient method, Mann’s iteration method, hybrid steepest-descent method, and vis- cosity approximation method (including Halpern’s iteration method). Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is derived.