  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 weights 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.
