On the convergence analysis of the alternating direction method of multipliers with three blocks
type: Item
instance of: scholarly article
title: On the convergence analysis of the alternating direction method of multipliers with three blocks
zbMATH Open document ID: 1302.90148
DOI: 10.1155/2013/183961
author: Caihua Chen
author: Yuan Shen
author: Yanfei You
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: We consider a class of linearly constrained separable convex programming problems whose objective functions are the sum of three convex functions without coupled variables. For those problems, \textit{D. Han} and \textit{X. Yuan} [J. Optim. Theory Appl. 155, No. 1, 227--238 (2012; Zbl 1255.90093)] have shown that the sequence generated by the alternating direction method of multipliers (ADMM) with three blocks converges globally to their KKT points under some technical conditions. In this paper, a new proof of this result is found under new conditions which are much weaker than Han and Yuan's assumptions. Moreover, in order to accelerate the ADMM with three blocks, we also propose a relaxed ADMM involving an additional computation of optimal step size and establish its global convergence under mild conditions.
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 6306112
zbMATH Keywords: separable convex programming problems
zbMATH Keywords: KKT points
zbMATH Keywords: optimal step size
zbMATH Keywords: global convergence
Wikidata QID: Q58915479
describes a project that uses: RASL
describes a project that uses: Yall1
describes a project that uses: RecPF
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/183961
OpenAlex ID: W2009378447
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description: scientific article; zbMATH DE number 6306112