Extragradient algorithms for solving equilibrium problems on Hadamard manifolds

Abstract

In this paper, we introduce three adaptive extragradient-based algorithms for solving equilibrium problems in Hadamard manifolds. The proposed algorithms can work adaptively without requiring the prior information about the Lipschitz constants of the bifunctions involved. Moreover, the iterative sequences generated by the suggested algorithms converge to the solutions of the equilibrium problems when the bifunctions are pseudomonotone and Lipschitz continuous. We also establish the global error bounds and R-linear convergence rates of the proposed algorithms in the case that the bifunctions involved are strongly pseudomonotone. Finally, a fundamental numerical example is given to illustrate the theoretical findings.