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In this paper, we introduce an inertial proximal method for solving a bilevelproblem involving two monotone equilibrium bifunctions in Hilbert spaces. Undersuitable conditions and without any restrictive assumption on the trajectories,the weak and strong convergence of the sequence generated by the iterativemethod are established. Two particular cases illustrating the proposed methodare thereafter discussed with respect to hierarchical minimization problems andequilibrium problems under saddle point constraint. Furthermore, a numericalexample is given to demonstrate the implementability of our algorithm. Thealgorithm and its convergence results improve and develop previous results inthe field.

Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems