This paper presents an extragradient-like method for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition on Hadamard manifolds. The algorithm only needs to know the existence of the Lipschitz-type constants of the bifunction, and the stepsize of each iteration is determined by the adjacent iterations. Convergence of the algorithm is analyzed, and its application to variational inequalities is also provided. Finally, several experiments are made to verify the effectiveness of the algorithms.

中文翻译：

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Hadamard流形上伪montone平衡问题的类梯度方法

本文提出了一种类似梯度的方法来解决Hadamard流形上具有Lipschitz型条件的拟单调平衡问题。该算法只需要知道双函数的Lipschitz型常数的存在，并且每个迭代的步长由相邻的迭代确定。分析了该算法的收敛性，并提供了其在变分不等式中的应用。最后，进行了几次实验以验证算法的有效性。