For solving monotone inclusion problems, we propose an inertial under-relaxed version of the relative-error hybrid proximal extragradient method. We study the asymptotic convergence of the method, as well as its nonasymptotic global convergence rates in terms of iteration complexity. We analyze the new method under more flexible assumptions than existing ones, both on the extrapolation and on the relative-error parameters. The approach is applied to two types of forward-backward type methods for solving structured monotone inclusions.

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关于不精确的相对误差混合近端引理，具有惯性效应的Teng和Tseng修正的正反方法

为了解决单调包含问题，我们提出了一种相对误差混合近端超梯度方法的惯性欠松弛版本。我们研究该方法的渐近收敛性，以及它在迭代复杂度方面的非渐近全局收敛速度。在外推和相对误差参数上，我们在比现有假设更灵活的假设下分析新方法。该方法适用于两种类型的前进-后退类型方法，用于解决结构化的单调包含。