NDLI: DLM: Decentralized Linearized Alternating Direction Method of Multipliers

Content Provider	IEEE Xplore Digital Library
Author	Qing Ling Wei Shi Gang Wu Ribeiro, A.
Copyright Year	1991
Abstract	This paper develops the Decentralized Linearized Alternating Direction Method of Multipliers (DLM) that minimizes a sum of local cost functions in a multiagent network. The algorithm mimics operation of the decentralized alternating direction method of multipliers (DADMM) except that it linearizes the optimization objective at each iteration. This results in iterations that, instead of successive minimizations, implement steps whose cost is akin to the much lower cost of the gradient descent step used in the distributed gradient method (DGM). The algorithm is proven to converge to the optimal solution when the local cost functions have Lipschitz continuous gradients. Its rate of convergence is shown to be linear if the local cost functions are further assumed to be strongly convex. Numerical experiments in least squares and logistic regression problems show that the number of iterations to achieve equivalent optimality gaps are similar for DLM and ADMM and both much smaller than those of DGM. In that sense, DLM combines the rapid convergence of ADMM with the low computational burden of DGM.
Sponsorship	IEEE Signal Processing Society
Starting Page	4051
Ending Page	4064
Page Count	14
File Size	3590095
File Format	PDF
ISSN	1053587X
Volume Number	63
Issue Number	15
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Cost function Convergence Signal processing algorithms Minimization Gradient methods Eigenvalues and eigenfunctions multiagent network Decentralized optimization linearized alternating direction method of multipliers
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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