Inertial forward-reflected-backward method for solving bilevel variational inequality problem

We introduce an inertial forward-reflected-backward method for solving the bilevel variational inequality problem. Our method involves a single projection onto the feasible set and one functional evaluation, which makes it cost-effective and efficient. The inertial technique in our algorithm improves its speed of convergence, and hence our algorithm performs faster than methods without inertial effect. Under moderate conditions, we obtain strong convergence of our algorithm. Lastly, we highlight the superior performance of our algorithm in comparison with other algorithms in the literature through our numerical experiments.