TY - GEN
T1 - A block coordinate descent method of multipliers
T2 - 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
AU - Hong, Mingyi
AU - Chang, Tsung Hui
AU - Wang, Xiangfeng
AU - Razaviyayn, Meisam
AU - Ma, Shiqian
AU - Luo, Zhi Quan
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014
Y1 - 2014
N2 - In this paper, we consider a nonsmooth convex problem with linear coupling constraints. Problems of this form arise in many modern large-scale signal processing applications including the provision of smart grid networks. In this work, we propose a new class of algorithms called the block coordinate descent method of multipliers (BCDMM) to solve this family of problems. The BCDMM is a primal-dual type of algorithm. It optimizes an (approximate) augmented Lagrangian of the original problem one block variable per iteration, followed by a gradient update for the dual variable. We show that under certain regularity conditions, and when the order for which the block variables are either updated in a deterministic or a random fashion, the BCDMM converges to the set of optimal solutions. The effectiveness of the algorithm is illustrated using large-scale basis pursuit and smart grid problems.
AB - In this paper, we consider a nonsmooth convex problem with linear coupling constraints. Problems of this form arise in many modern large-scale signal processing applications including the provision of smart grid networks. In this work, we propose a new class of algorithms called the block coordinate descent method of multipliers (BCDMM) to solve this family of problems. The BCDMM is a primal-dual type of algorithm. It optimizes an (approximate) augmented Lagrangian of the original problem one block variable per iteration, followed by a gradient update for the dual variable. We show that under certain regularity conditions, and when the order for which the block variables are either updated in a deterministic or a random fashion, the BCDMM converges to the set of optimal solutions. The effectiveness of the algorithm is illustrated using large-scale basis pursuit and smart grid problems.
UR - http://www.scopus.com/inward/record.url?scp=84905270262&partnerID=8YFLogxK
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U2 - 10.1109/ICASSP.2014.6855096
DO - 10.1109/ICASSP.2014.6855096
M3 - Conference contribution
AN - SCOPUS:84905270262
SN - 9781479928927
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 7689
EP - 7693
BT - 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 4 May 2014 through 9 May 2014
ER -