TY - JOUR
T1 - On the O(1/N) Convergence Rate of the Douglas–Rachford Alternating Direction Method
AU - He, Bingsheng
AU - Yuan, Xiaoming
N1 - Funding information:
Departement of Mathematics, Nanjing University, Nanjing 210093, China ([email protected]). This author’s work was supported by NSFC grants 10971095 and 91130007, the Cultivation Fund of KSTIP-MOEC 708044, and the MOEC fund 20110091110004.
t Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (xmyuan@hkbu. edu.hk). This author’s work was supported by the Hong Kong General Research Fund 203311 and by HKBU grant FRG2/10-11/069.
Publisher copyright:
Copyright © 2012 Society for Industrial and Applied Mathematics
PY - 2012/4/10
Y1 - 2012/4/10
N2 - 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.
AB - 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.
KW - Alternating direction method
KW - Convergence rate
KW - Convex programming
KW - Split inexact Uzawa method
KW - Variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=84861398963&partnerID=8YFLogxK
U2 - 10.1137/110836936
DO - 10.1137/110836936
M3 - Review article
AN - SCOPUS:84861398963
SN - 0036-1429
VL - 50
SP - 700
EP - 709
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 2
ER -