Paper Info
Title
A block coordinate descent method of multipliers: Convergence analysis and applications
Abstract
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.
Year
DOI
Venue
2014
10.1109/ICASSP.2014.6855096
ICASSP
Keywords
Field
DocType
smart grid networks,bcdmm,convex programming,nonsmooth convex problem,augmented lagrangian,large-scale basis pursuit,gradient methods,smart power grids,block variables,primal-dual type algorithm,large-scale signal processing,linear coupling constraints,block coordinate descent method of multipliers,gradient update,convex functions,convergence,approximation algorithms,optimization,smart grids,minimization
Convergence (routing),Stochastic gradient descent,Mathematical optimization,Smart grid,Computer science,Basis pursuit,Random coordinate descent,Augmented Lagrangian method,Coordinate descent,Convex optimization
Conference
ISSN
Citations 
PageRank 
1520-6149
4
0.42
References 
Authors
14
6
Name
Order
Citations
PageRank
Mingyi Hong1153391.29
Tsung-Hui Chang2114272.18
Xiangfeng Wang328021.75
Meisam Razaviyayn491344.38
Shiqian Ma5106863.48
Zhi-Quan Luo67506598.19