Analysis of distributed ADMM algorithm for consensus optimisation over lossy networks

Alternating direction method of multipliers (ADMM) is a popular convex optimisation algorithm, which is implemented in a distributed manner. Applying this algorithm to consensus optimisation problem, where a number of agents cooperatively try to solve an optimisation problem using locally available...

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Published in:IET signal processing Vol. 12; no. 6; pp. 786 - 794
Main Authors: Majzoobi, Layla, Shah-Mansouri, Vahid, Lahouti, Farshad
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 01.08.2018
Subjects:
alternating direction method of multipliers
computational complexity
computational resource requirements
consensus optimisation problem
convex optimisation algorithm
convex programming
distributed ADMM algorithm
distributed algorithms
lossy network
network connectivity
Research Article
storage requirements
lossy network
convex optimisation algorithm
alternating direction method of multipliers
distributed algorithms
distributed ADMM algorithm
network connectivity
convex programming
storage requirements
consensus optimisation problem
computational complexity
computational resource requirements
ISSN:1751-9675, 1751-9683, 1751-9683
Online Access:Get full text
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Abstract Alternating direction method of multipliers (ADMM) is a popular convex optimisation algorithm, which is implemented in a distributed manner. Applying this algorithm to consensus optimisation problem, where a number of agents cooperatively try to solve an optimisation problem using locally available data, leads to a fully distributed algorithm which relies on local computations and communication between neighbours. In this study, the authors analyse the convergence of the distributed ADMM algorithm for solving a consensus optimisation problem over a lossy network, whose links are subject to failure. They present and analyse two different distributed ADMM-based algorithms. The algorithms are different in their network connectivity, storage and computational resource requirements. The first one converges over a sequence of networks which are not the same but remains connected over all iterations. The second algorithm is convergent over a sequence of different networks whose union is connected. The former algorithm, compared to the latter, has lower computational complexity and storage requirements. Numerical experiments confirm the proposed theoretical analysis.
AbstractList Alternating direction method of multipliers (ADMM) is a popular convex optimisation algorithm, which is implemented in a distributed manner. Applying this algorithm to consensus optimisation problem, where a number of agents cooperatively try to solve an optimisation problem using locally available data, leads to a fully distributed algorithm which relies on local computations and communication between neighbours. In this study, the authors analyse the convergence of the distributed ADMM algorithm for solving a consensus optimisation problem over a lossy network, whose links are subject to failure. They present and analyse two different distributed ADMM-based algorithms. The algorithms are different in their network connectivity, storage and computational resource requirements. The first one converges over a sequence of networks which are not the same but remains connected over all iterations. The second algorithm is convergent over a sequence of different networks whose union is connected. The former algorithm, compared to the latter, has lower computational complexity and storage requirements. Numerical experiments confirm the proposed theoretical analysis.
Author Shah-Mansouri, Vahid
Majzoobi, Layla
Lahouti, Farshad
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  organization: 2Electrical Engineering Department, California Institute of Technology, Pasadena, USA
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Keywords lossy network
convex optimisation algorithm
alternating direction method of multipliers
distributed algorithms
distributed ADMM algorithm
network connectivity
convex programming
storage requirements
consensus optimisation problem
computational complexity
computational resource requirements
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Snippet Alternating direction method of multipliers (ADMM) is a popular convex optimisation algorithm, which is implemented in a distributed manner. Applying this...
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wiley
iet
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StartPage 786
SubjectTerms alternating direction method of multipliers
computational complexity
computational resource requirements
consensus optimisation problem
convex optimisation algorithm
convex programming
distributed ADMM algorithm
distributed algorithms
lossy network
network connectivity
Research Article
storage requirements
Title Analysis of distributed ADMM algorithm for consensus optimisation over lossy networks
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Volume 12
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