A two-step inertial algorithm for solving equilibrium problems on Hadamard manifolds

In the context of Hadamard manifolds, we develop a two-step inertial subgradient extragradient method for approximating solutions of equilibrium problems involving a pseudomonotone operator. To avoid dependency of the step-size on the Lipschitz constant of the underlying operator, we propose an iterative method with a self-adaptive step size that can increase with each iteration. Furthermore, we prove a strong convergence result concerning the sequence generated by our two-step inertial subgradient extragradient method in the setting of Hadamard manifolds. To illustrate the performance of our iterative method relative to other methods of a similar nature, we provide some numerical examples. The results presented in this article are new in this space and extend many related findings in the literature.