Mathematics > Optimization and Control
[Submitted on 31 Oct 2022 (v1), last revised 1 Apr 2023 (this version, v2)]
Title:Distributed optimization on directed graphs based on inexact ADMM with partial participation
View PDFAbstract:We consider the problem of minimizing the sum of cost functions pertaining to agents over a network whose topology is captured by a directed graph (i.e., asymmetric communication). We cast the problem into the ADMM setting, via a consensus constraint, for which both primal subproblems are solved inexactly. In specific, the computationally demanding local minimization step is replaced by a single gradient step, while the averaging step is approximated in a distributed fashion. Furthermore, partial participation is allowed in the implementation of the algorithm. Under standard assumptions on strong convexity and Lipschitz continuous gradients, we establish linear convergence and characterize the rate in terms of the connectivity of the graph and the conditioning of the problem. Our line of analysis provides a sharper convergence rate compared to Push-DIGing. Numerical experiments corroborate the merits of the proposed solution in terms of superior rate as well as computation and communication savings over baselines.
Submission history
From: Dingran Yi [view email][v1] Mon, 31 Oct 2022 11:55:16 UTC (710 KB)
[v2] Sat, 1 Apr 2023 02:34:26 UTC (565 KB)
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