The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model.

中文翻译：

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惯性次梯度超梯度算法扩展到拟单调平衡问题

本文介绍了一种具有自适应步长的惯性超梯度次梯度方法，用于解决实际希尔伯特空间中的平衡问题。在双函数为伪单调和Lipchitz连续的条件下，该方法的收敛性较弱。当双功能为强伪单调且Lipchitz连续时，也会给出线性收敛。使用包括实际应用到纳什-古诺寡头垄断电力市场均衡模型在内的测试问题，给出了与其他相关惯性方法的数值实现和比较。