## Abstract and Applied Analysis

### On the Convergence Analysis of the Alternating Direction Method of Multipliers with Three Blocks

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 183961, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450485

Digital Object Identifier
doi:10.1155/2013/183961

Mathematical Reviews number (MathSciNet)
MR3121502

Zentralblatt MATH identifier
1302.90148

#### Citation

Chen, Caihua; Shen, Yuan; You, Yanfei. On the Convergence Analysis of the Alternating Direction Method of Multipliers with Three Blocks. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 183961, 7 pages. doi:10.1155/2013/183961. https://projecteuclid.org/euclid.aaa/1393450485

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