Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error

Alternating direction method of multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting, agents locally estimate the optimal solution of an optimization problem and exchange messages with their neig...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 67; no. 7; pp. 1774 - 1784
Main Authors: Majzoobi, Layla, Lahouti, Farshad, Shah-Mansouri, Vahid
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additives
ADMM algorithm
Algorithms
Computational geometry
consensus optimization
Convergence
Convex functions
Convexity
Iterative methods
Linear programming
Lower bounds
node error
Nodes
Noise measurement
Optimization
Signal processing algorithms
steady-state error
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:Alternating direction method of multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting, agents locally estimate the optimal solution of an optimization problem and exchange messages with their neighbors over a connected network. The distributed algorithms are typically exposed to different types of errors in practice, e.g., due to quantization or communication noise or loss. We here focus on analyzing the convergence of distributed ADMM for consensus optimization in the presence of additive random node error, in which case the nodes communicate a noisy version of their latest estimate of the solution to their neighbors in each iteration. We present analytical upper and lower bounds on the mean-squared steady-state error of the algorithm in case the local objective functions are strongly convex and have Lipschitz continuous gradients. In addition, we show that when the local objective functions are convex and the additive node error is bounded, the estimation error of the noisy ADMM for consensus optimization is also bounded. Numerical results are provided, which demonstrates the effectiveness of the presented analyses and shed light on the role of the system and network parameters on performance.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2896266