LAUSR

ABSTRACT In this paper, we present two algorithms for solving equilibrium problems on Hadamard manifolds. The two algorithms use the extragradient model and the golden ratio model, respectively, which are two classical models for solving the equilibrium problem in linear space. In each iteration, the step sizes of the two algorithms only depend on the value of the initial parameters and the information of the current iteration. Moreover, compared with the first algorithm, the second algorithm only needs to solve one quadratic programming problem per iteration, which can greatly reduce the computational complexity of the algorithm when the structure of the feasible region is complex. Under mild conditions, we prove that the sequence generated by each algorithm converges to some equilibrium point. Also, we use an experiment to verify the effectiveness of the algorithms.