The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions
type: Item
instance of: scholarly article
title: The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions
zbMATH Open document ID: 1197.47077
author: Abdellatif Moudafi
published in: Applied Mathematics Letters
publication date: 2010-05-05T00:00:00Z
review text: Let \(A\) and \(B\) be two maximal monotone operators on a real Hilbert space \(H\) and let \(\mu, \beta\in (0,\infty).\) This paper is concerned with the convergence analysis of alternating inertial algorithms for inclusion problems of the following type \[ \text{find } (x^*,y^*)\in H\times H \text{ such that } (0,0)\in (I-R+(\beta^{-1}A\times\mu^{-1}B)(x^*,y^*), \] where \(I\) is the identity mapping and \(R: (x,y)\mapsto (y,x).\) The obtained results generalize existing results in the literature. An application to equilibrium problems is also proposed.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J22
zbMATH DE Number: 5704058
zbMATH Keywords: maximal monotone operators
zbMATH Keywords: alternating proximal algorithm
zbMATH Keywords: alternating projection methods
zbMATH Keywords: joint minimization
zbMATH Keywords: equilibrium problems
MaRDI profile type: Publication
full work available at URL: j.aml.2010.01.023
OpenAlex ID: W2017742764
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DOI: 10.1016/J.AML.2010.01.023
description: scientific article; zbMATH DE number 5704058