Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems

Abstract

In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.