Convergence rate analysis of distributed optimization with projected subgradient algorithm

• Autores: Shuai Liu, Zhirong Qiu-, Lihua Xie
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 83, 2017, págs. 162-169
• Idioma: inglés
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• Resumen

  • Abstract 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 O ( 1 ∕ k ) can be achieved with a step size O ( 1 ∕ k ) .