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Subgradient averaging for multi-agent optimisation with different constraint sets
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DOI：10.1016/j.automatica.2021.109738.png)
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Abstract
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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 eta/k+1, eta > 0. We also analyse this scheme under a step size choice of eta/root k+1, eta > 0, and establish a convergence rate of O(ln k/root k) in objective value. To demonstrate the efficacy of the proposed method, we investigate a robust regression problem and an l(2) regression problem with regularisation. (C) 2021 Elsevier Ltd. All rights reserved.
Keywords:
Distributed optimisation
Multi-agent networks
Parallel algorithms
Subgradient methods
Consensus
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