The paper introduces an one-step optimization method for solving a monotone equilibrium problem including a Lipschitz-type condition in a Hilbert space. The method uses variable stepsizes and is constructed by the proximal-like mapping associated with the cost bifunction and incorporated with regularization terms. Comparing with the extragradient-like methods, our new method has an elegant and simple structure with a cheap computation over each iteration. By an appropriate choice of stepsizes and regularization parameters, we establish the strong convergence of the iterative sequence generated by the method to a solution of the considered equilibrium problem. We also show the numerical behavior of our new method and illustrate the computational effectiveness of it over other methods via experiments.

本文介绍了一种单调平衡问题的单调优化方法，该问题包括希尔伯特空间中的 Lipschitz 型条件。该方法使用可变步长，并由与成本双函数相关联的类似近端的映射构造，并结合正则化项。与类外梯度方法相比，我们的新方法结构优雅简单，每次迭代的计算成本低。通过适当的步骤和正则化参数的选择，我们确定了该方法生成的迭代序列的强收敛，以对考虑的平衡问题的解决方案。我们还展示了我们的新方法的数值行为，并通过实验说明了它相对于其他方法的计算有效性。