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

Maicon Marques Alves(maicon.alves***at***ufsc.br)
Raul Marcavillaca(rtm1111***at***hotmail.com)

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.

Keywords: inertial, relaxed, proximal point method, HPE method, pointwise, ergodic, iteration-complexity, forward-backward algorithm, Tseng's modified forward-backward algorithm

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 12/05/2018
Entry Accepted: 12/05/2018
Entry Last Modified: 12/05/2018

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