A relaxed projection method for solving bilevel variational inequality problems

In this work, we present a new relaxed projection approach to solve bilevel variational inequality problems in a real Hilbert space. First, we introduce a solution mapping of the variational inequality problem and analyze its strongly quasi-nonexpansiveness. Next, by using this mapping we present a relaxed projection algorithm for solving bilevel variational inequality problems. Under pseudomonotonicity assumptions on the cost mappings, strong convergence of iteration sequences is proved. Finally, we give some numerical results to illustrate the proposed algorithm.