In this paper, we introduce some new accelerated hybrid algorithms for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition in a Hilbert space. The algorithms are constructed around the extragradient method, the inertial technique, the hybrid (or outer approximation) method, and the shrinking projection method. The algorithms are designed to work either with or without the prior knowledge of the Lipschitz-type constants of bifunction. Theorems of strong convergence are established under mild conditions. The results in this paper generalize, extend, and improve some known results in the field. Finally, several of numerical experiments are performed to support the obtained theoretical results.

中文翻译：

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求解拟单调平衡问题的加速混合方法

在本文中，我们介绍了一些新的加速混合算法，用于解决希尔伯特空间中具有Lipschitz型条件的伪单调平衡问题。这些算法是围绕超梯度方法，惯性技术，混合（或外部近似）方法和收缩投影方法构建的。该算法设计为在有或没有双功能Lipschitz型常数的先验知识的情况下工作。强收敛定理是在温和条件下建立的。本文的结果概括，扩展和改进了该领域中的一些已知结果。最后，进行了一些数值实验以支持获得的理论结果。