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In this paper, the Alternating Direction Method of Multipliers (ADMM) is investigated for distributed optimization problems in a networked multi-agent system. In particular, a new adaptive-gain ADMM algorithm is derived in a closed form and under the standard convex property in order to greatly speed up convergence of ADMM-based distributed optimization. Using Lyapunov direct approach, the proposed solution embeds control gains into weighted network matrix among the agents and uses those<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/access.2020.2989402">doi:10.1109/access.2020.2989402</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7ssklo3qzrbmzioouo67hvcjsi">fatcat:7ssklo3qzrbmzioouo67hvcjsi</a> </span>
more »... as adaptive penalty gains in the augmented Lagrangian. It is shown that the proposed closed loop gain adaptation scheme significantly improves the convergence time of underlying ADMM optimization. Convergence analysis is provided and simulation results are included to demonstrate the effectiveness of the proposed scheme. INDEX TERMS Distributed optimization, ADMM, gain adaptation, rate of convergence, Lyapunov direct method. 80480 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020 ZHIHUA QU (Fellow, IEEE) received the Ph.D. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, in June 1990. Since then, he has been with the University of Central Florida (UCF), Orlando. He is currently the SAIC Endowed Professor with the with the College of Engineering and Computer Science, the Pegasus Professor and the Chair of Electrical and Computer Engineering, and the Founder and the Director of the RISES Cluster and FEEDER Center. His areas of expertise are nonlinear systems and control, with applications to energy, power systems, and autonomous vehicle systems. In energy systems, his research covers distributed energy resources, dynamic stability of power systems, antiislanding control and protection, distributed generation and load sharing control, distributed VAR compensation, distributed optimization, and cooperative control.
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