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On the Q-Linear Convergence of Distributed Generalized ADMM Under Non-Strongly Convex Function Components
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.ORCID iD: 0000-0001-6630-243X
2019 (English)In: IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, ISSN 2373-776X, Vol. 5, no 3, p. 442-453Article in journal (Refereed) Published
Abstract [en]

Solving optimization problems in multi-agent networks where each agent only has partial knowledge of the problem has become an increasingly important problem. In this paper, we consider the problem of minimizing the sum of n convex functions. We assume that each function is only known by one agent. We show that generalized distributed alternating direction method of multipliers (ADMM) converges Q-linearly to the solution of the mentioned optimization problem if the overall objective function is strongly convex but the functions known by each agent are allowed to be only convex. Establishing Q-linear convergence allows for tracking statements that cannot be made if only R-linear convergence is guaranteed. In other words, in scenarios in which the objective functions are time-varying at the same scale as the algorithm is updated R-linear convergence is typically insufficient. Further, we establish the equivalence between generalized distributed ADMM and proximal exact first-order algorithm (P-EXTRA) for a sub-set of mixing matrices. This equivalence yields insights in the convergence of P-EXTRA when overshooting to accelerate convergence.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2019. Vol. 5, no 3, p. 442-453
Keywords [en]
Decentralized optimization, convex optimization, ADMM, Q-linear convergence, EXTRA
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-256237DOI: 10.1109/TSIPN.2019.2892055ISI: 000478679200004Scopus ID: 2-s2.0-85059803269OAI: oai:DiVA.org:kth-256237DiVA, id: diva2:1363185
Note

QC 20191022

Available from: 2019-10-22 Created: 2019-10-22 Last updated: 2019-12-11Bibliographically approved

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Maros, MarieJaldén, Joakim

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  • apa
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