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Convergence rate analysis of distributed optimization with projected subgradient algorithm
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DOI：10.1016/j.automatica.2017.06.011.png)
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In this paper, we revisit the consensus-based projected subgradient algorithm proposed for a common set constraint. We show that the commonly adopted non-summable and square-summable diminishing step sizes of subgradients can be relaxed to be only non-summable, if the constrained optimum set is bounded. More importantly, for a strongly convex aggregate cost with different types of step sizes, we provide a systematical analysis to derive the asymptotic upper bound of convergence rates in terms of the optimum residual, and select the best step sizes accordingly. Our result shows that a convergence rate of 0(1/root k) can be achieved with a step size 0(1/k). (C) 2017 Elsevier Ltd. All rights reserved.
Keywords:
Distributed optimization
Subgradients
Convergence rate
Multi-agent systems
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