An accelerated subgradient extragradient algorithm for solving bilevel variational inequality problems involving non-Lipschitz operator

In this paper, an accelerated subgradient extragradient algorithm with a new non-monotonic step size is proposed to solve bilevel variational inequality problems involving non-Lipschitz continuous operator in Hilbert spaces. The proposed algorithm with a new non-monotonic step size has the advantage of requiring only one projection onto the feasible set during each iteration and does not require prior knowledge of the Lipschitz constant of the mapping involved. Under suitable and weaker conditions, the proposed algorithm achieves strong convergence. Some numerical tests are provided to demonstrate the efficiency and advantages of the proposed algorithm against existing related algorithms.