Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds

Abstract

Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution of the equilibrium problem without requiring the Lipschitz continuity of the bifunction or imposing additional conditions on the parameters. We establish convergence results for both algorithms and derive global error bounds along with $R$-linear convergence rates in cases where the bifunction is strongly pseudomonotone. Finally, we present numerical experiments to demonstrate the effectiveness of our methods.