Department of Mathematics
On the O(1/n) convergence rate of Douglas-Rachford alternating direction method
Alternating direction methods (ADMs) have been well studied in the literature, and they have found many efficient applications in various fields. In this note, we focus on the Douglas- Rachford ADM scheme proposed by Glowinski and Marrocco, and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number. The linearized version of this ADM scheme, which is known as the split inexact Uzawa method in the image processing literature, is also discussed. © 2012 Society for Industrial and Applied Mathematics.
Alternating direction method, Convergence rate, Convex programming, Split inexact Uzawa method, Variational inequalities
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
He, Bingsheng, and Xiaoming Yuan. "On the O(1/n) convergence rate of Douglas-Rachford alternating direction method." SIAM Journal on Numerical Analysis 50.2 (2012): 700-709.