Inexact Inertial Proximal Algorithm for Maximal Monotone Operators-Reference-Cited by-同舟云学术

Inexact Inertial Proximal Algorithm for Maximal Monotone Operators

Published:2015-06-01 Issue:2 Volume:23 Page:133-146
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Khatibzadeh Hadi¹,Ranjbar Sajad²

Affiliation:

1. Department of Mathematics, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran (Islamic Republic of)

2. Zarghan Branch, Islamic Azad University, Zarghan, Iran (Islamic Republic of)

Abstract

Abstract In this paper, convergence of the sequence generated by the inexact form of the inertial proximal algorithm is studied. This algorithm which is obtained by the discretization of a nonlinear oscillator with damping dynamical system, has been introduced by Alvarez and Attouch (2001) and Jules and Maingé (2002) for the approximation of a zero of a maximal monotone operator. We establish weak and strong convergence results for the inexact inertial proximal algorithm with and without the summability assumption on errors, under different conditions on parameters. Our theorems extend the results on the inertial proximal algorithm established by Alvarez and Attouch (2001) and rules and Maingé (2002) as well as the results on the standard proximal point algorithm established by Brézis and Lions (1978), Lions (1978), Djafari Rouhani and Khatibzadeh (2008) and Khatibzadeh (2012). We also answer questions of Alvarez and Attouch (2001).

Publisher

Walter de Gruyter GmbH

Reference16 articles.

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