A NEW INERTIAL RELAXED TSENG EXTRGRADIENT METHOD FOR PROBLEMS IN HILBERT SPACES

In this paper, we introduce an inertial relaxed Tseng extragradient method involving only a single projection for solving bilevel variational inequality problems with Lipschitz continuous and quasimonotone mapping in Hilbert spaces. Under some mild standard assumptions, we obtain a strong convergence result for solving bilevel quasimonotone variational inequality problems. The main advan-tages of the proposed iterative method are that it requires only one projection onto the feasible set and the use self adaptive step-size rule based on operator knowledge rather than a Lipschitz constant or some line search method. Moreover, some interesting preliminary numerical experiments and comparisons were presented.