A Partition-Based Implementation of the Relaxed ADMM for Distributed Convex Optimization over Lossy Networks

In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents, one for each agent. Specifically the local cost stored by e...

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Bibliographic Details
Published inProceedings of the IEEE Conference on Decision & Control pp. 3379 - 3384
Main Authors Bastianello, N., Carli, R., Schenato, L., Todescato, M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2018
Subjects
ADMM
Convergence
Convex functions
distributed optimization
Nickel
operator theory
Optimization
partition-based optimization
Partitioning algorithms
Peaceman-Rachford operator
Peer-to-peer computing
splitting methods
Trajectory
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ISSN2576-2370
DOI10.1109/CDC.2018.8619729

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Summary:In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents, one for each agent. Specifically the local cost stored by each node is in general a function of both the state of the node and the states of its neighbors, a framework that we refer to as 'partition-based' optimization. This framework presents a great flexibility and can be adapted to a large number of different applications. By recasting the problem into an operator theoretical framework, the proposed algorithm is shown to be provably robust against random packet losses that might occur in the communication between neighboring nodes. Finally, the effectiveness of the proposed algorithm is confirmed by a set of compelling numerical simulations run over random geometric graphs subject to i.i.d. random packet losses.
ISSN:2576-2370
DOI:10.1109/CDC.2018.8619729