Subgradient averaging for multi-agent optimisation with different constraint sets

We consider a multi-agent setting with agents exchanging information over a possibly time-varying network, aiming at minimising a separable objective function subject to constraints. To achieve this objective we propose a novel subgradient averaging algorithm that allows for non-differentiable objec...

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Veröffentlicht in:Automatica (Oxford) Jg. 131; S. 109738
Hauptverfasser: Romao, Licio, Margellos, Kostas, Notarstefano, Giuseppe, Papachristodoulou, Antonis
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.09.2021
Schlagworte:
Consensus
Distributed optimisation
Multi-agent networks
Parallel algorithms
Subgradient methods
Subgradient methods
Multi-agent networks
Parallel algorithms
Consensus
Distributed optimisation
ISSN:0005-1098, 1873-2836
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Zusammenfassung:We consider a multi-agent setting with agents exchanging information over a possibly time-varying network, aiming at minimising a separable objective function subject to constraints. To achieve this objective we propose a novel subgradient averaging algorithm that allows for non-differentiable objective functions and different constraint sets per agent. Allowing different constraints per agent simultaneously with a time-varying communication network constitutes a distinctive feature of our approach, extending existing results on distributed subgradient methods. To highlight the necessity of dealing with a different constraint set within a distributed optimisation context, we analyse a problem instance where an existing algorithm does not exhibit a convergent behaviour if adapted to account for different constraint sets. For our proposed iterative scheme we show asymptotic convergence of the iterates to a minimum of the underlying optimisation problem for step sizes of the form ηk+1, η>0. We also analyse this scheme under a step size choice of ηk+1, η>0, and establish a convergence rate of O(lnkk) in objective value. To demonstrate the efficacy of the proposed method, we investigate a robust regression problem and an ℓ2 regression problem with regularisation.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2021.109738