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In this paper, we propose and study the asymptotic convergence andnonasymptotic global convergence rates (iteration-complexity) of an inertialunder-relaxed version of the relative-error hybrid proximal extragradient (HPE)method for solving monotone inclusion problems. We analyze the proposed methodunder more flexible assumptions than existing ones on the extrapolation andrelative-error parameters. As applications, we propose and/or study inertialunder-relaxed forward-backward and Tseng's modified forward-backward typemethods for solving structured monotone inclusions.

On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng's modified forward-backward methods with inertial effects