Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions

Naoki HAYASHI  Yuichi KAJIYAMA  Shigemasa TAKAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.2   pp.435-442
Publication Date: 2020/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019MAP0008
Type of Manuscript: Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)
distributed optimization,  cooperative control,  data-rate constraints,  

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This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.