Distributed primal-dual optimisation method with uncoordinated time-varying step-sizes

Ping Liu, Huaqing Li, Xiangguang Dai and Qi Han

International Journal of Systems Science, 2018, vol. 49, issue 6, 1256-1272

Abstract: This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm.

Date: 2018
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DOI: 10.1080/00207721.2018.1442886

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