On Inexact Relative-Error Hybrid Proximal Extragradient, Forward-Backward and Tseng’s Modified Forward-Backward Methods with Inertial Effects

Abstract

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.