A block coordinate descent method of multipliers: Convergence analysis and applications

Mingyi Hong, Tsung Hui Chang, Xiangfeng Wang, Meisam Razaviyayn, Shiqian Ma, Zhi-Quan Luo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7689-7693
Number of pages5
ISBN (Print)9781479928927
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy
Duration: May 4 2014May 9 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
CountryItaly
CityFlorence
Period5/4/145/9/14

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Hong, M., Chang, T. H., Wang, X., Razaviyayn, M., Ma, S., & Luo, Z-Q. (2014). A block coordinate descent method of multipliers: Convergence analysis and applications. In 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 (pp. 7689-7693). [6855096] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2014.6855096