A self-adaptive inertial subgradient extragradient algorithm for solving bilevel equilibrium problems

In this paper, we introduce an inertial subgradient extragradient method with a self-adaptive technique for solving bilevel equilibrium problem in real Hilbert spaces. The algorithm is designed such that its stepsize is chosen without the need for prior estimates of the Lipschitz-like constants of the upper level bifunction nor a line searching procedure. This provides computational advantages to the algorithm compared with other similar methods in the literature. We prove a strong convergence result for the sequences generated by our algorithm under suitable conditions. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.