Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems

Mingyi Hong, Zhi-Quan Luo, Meisam Razaviyayn

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

44 Scopus citations

Abstract

In this paper, we analyze the behavior of the alternating direction method of multipliers (ADMM), for solving a family of nonconvex problems. Our focus is given to the well-known consensus and sharing problems, both of which have wide applications in signal processing. We show that in the presence of nonconvex objective function, classical ADMM is able to reach the set of stationary solutions for these problems, if the stepsize is chosen large enough. An interesting consequence of our analysis is that the ADMM is convergent for a family of sharing problems, regardless of the number of blocks or the convexity of the objective function. Our analysis is broadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules.

Original languageEnglish (US)
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3836-3840
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - Aug 4 2015
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: Apr 19 2014Apr 24 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Other

Other40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
CountryAustralia
CityBrisbane
Period4/19/144/24/14

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