期刊
AUTOMATICA
卷 94, 期 -, 页码 55-62出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2018.04.010
关键词
Distributed optimization; Augmented Lagrange method; Convergence analysis; Factorization of weighted Laplacian
资金
- Funds of the National Natural Science Foundation of China [61621004, 61420106016]
- Research Fund of State Key Laboratory of Synthetical Automation for Process Industries [2013ZCX01]
In this paper, the augmented Lagrange (AL) algorithm for distributed optimization is studied. Compared with the existing results, this paper uses different techniques, including the factorization of weighted Laplacian and the spectral decomposition technique, to prove the linear convergence of the AL algorithm, and simultaneously provides a novel description on the convergence rate. First, by using an important factorization of weighted Laplacian, it is proved that the linear convergence of the AL algorithm can be achieved via a simplified analysis procedure. Within this framework, a novel quantitative description on the convergence rate is then provided based on spectral decomposition technique. Meanwhile, by determining the monotonicity of an auxiliary function, a connection between convergence rate, step size and edge weights is established. Finally, simulation examples illustrate the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.
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