In this work, we develop a quasi-Newton-type method for equilibrium problems based on the proximal Newton-type structure given in Santos et al. (Optimization Letters 12(5), 997-1009, 2018). We consider a family of matrices verifying a bounded deterioration property. We prove that the sequence generated by the algorithm is well defined and under suitable assumptions we establish the linear convergence of the algorithm. Numerical experiments are reported.

中文翻译：

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平衡问题的拟牛顿型方法

在这项工作中，我们基于 Santos 等人给出的近端牛顿型结构开发了一种用于平衡问题的拟牛顿型方法。（优化快报 12(5), 997-1009, 2018）。我们考虑验证有界退化特性的矩阵族。我们证明算法生成的序列是明确定义的，并且在适当的假设下我们建立了算法的线性收敛。报告了数值实验。