Campus Units

Industrial and Manufacturing Systems Engineering

Document Type

Article

Publication Version

Published Version

Publication Date

2016

Journal or Book Title

SIAM Journal on Optimization

Volume

26

Issue

1

First Page

337

Last Page

364

DOI

10.1137/140990309

Abstract

The alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems, convex or nonconvex, in many engineering fields. However there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex. In this paper we analyze the convergence of the ADMM for solving certain nonconvex consensus and sharing problems. We show that the classical ADMM converges to the set of stationary solutions, provided that the penalty parameter in the augmented Lagrangian is chosen to be sufficiently large. For the sharing problems, we show that the ADMM is convergent regardless of the number of variable blocks. Our analysis does not impose any assumptions on the iterates generated by the algorithm and is broadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules.

Comments

This is an article from SIAM Journal on Optimization 26 (2016): 337, doi:10.1137/140990309 Posted with permission.

Copyright Owner

SIAM

Language

en

File Format

application/pdf

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