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arXiv · 1812.02138

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

M. Marques Alves·Raul T. Marcavillaca
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Abstract

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

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M. Marques Alves, Raul T. Marcavillaca. 2018-12-05. On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng's modified forward-backward methods with inertial effects. https://arxiv.org/abs/1812.02138

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