We propose a relaxed-inertial proximal point algorithm for solving equilibrium problems involving bifunctions which satisfy in the second variable a generalized convexity notion called strong quasiconvexity, introduced by Polyak (Sov Math Dokl 7:72–75, 1966). The method is suitable for solving mixed variational inequalities and inverse mixed variational inequalities involving strongly quasiconvex functions, as these can be written as special cases of equilibrium problems. Numerical experiments where the performance of the proposed algorithm outperforms one of the standard proximal point methods are provided, too.

中文翻译：

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非凸平衡问题的松弛惯性近点算法及其应用

我们提出了一种松弛惯性近点算法，用于解决涉及双函数的平衡问题，该双函数在第二个变量中满足称为强拟凸性的广义凸性概念，由 Polyak 引入（Sov Math Dokl 7:72–75, 1966）。该方法适用于求解涉及强拟凸函数的混合变分不等式和逆混合变分不等式，因为这些可以写成平衡问题的特例。还提供了数值实验，其中所提出的算法的性能优于标准近点方法之一。