In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consists of an inertial extrapolation process for speeding the rate of its convergence, a monotone nonincreasing stepsize rule, and a viscosity approximation method which guaranteed its strong convergence. More so, a strong convergence theorem is proved for the sequence generated by the algorithm under some mild conditions and without prior knowledge of the Lipschitz-like constants of the equilibrium bifunction. We further provide some numerical examples to illustrate the performance and accuracy of our method.

中文翻译：

---

拟单调平衡和常见不动点问题的自适应惯性次梯度超梯度方法

本文介绍了一种自适应惯性次梯度超梯度方法，用于求解真实希尔伯特空间中的伪单调平衡问题和公共不动点问题。该算法包括一个用于加快收敛速度​​的惯性外推过程，一个单调非递增步长规则以及一个保证其强收敛性的粘度逼近方法。更有什者，在某些温和条件下并且没有对平衡双功能的Lipschitz样常数的先验知识的情况下，证明了该算法生成的序列的强收敛定理。我们进一步提供一些数值示例来说明我们方法的性能和准确性。