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2013 On the Convergence Analysis of the Alternating Direction Method of Multipliers with Three Blocks
Caihua Chen, Yuan Shen, Yanfei You
Abstr. Appl. Anal. 2013(SI54): 1-7 (2013). DOI: 10.1155/2013/183961

Abstract

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, Han and Yuan (2012) 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.

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Caihua Chen. Yuan Shen. Yanfei You. "On the Convergence Analysis of the Alternating Direction Method of Multipliers with Three Blocks." Abstr. Appl. Anal. 2013 (SI54) 1 - 7, 2013. https://doi.org/10.1155/2013/183961

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1302.90148
MathSciNet: MR3121502
Digital Object Identifier: 10.1155/2013/183961

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI54 • 2013
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