Abstract
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.
Highlights
In the era of Internet of Things (IoT) and smart agents, the amount of data available in the network explodes in both size and complexity
To solve (1) using Alternating Direction Method of Multipliers (ADMM), we introduce a set of auxiliary variables, zji, which are the estimates of agent j’s variables by agent i [8]
The proposed gain adaptation technique is illustrated through simulations and in two parts
Summary
In the era of Internet of Things (IoT) and smart agents, the amount of data available in the network explodes in both size and complexity. In [21], the weighted network matrix is adaptively tuned to improve convergence in a consensusbased distributed problem framework using cooperative control This idea is used in [22] where a consensus based distributed ADMM is formulated with a predefined network structure, for which primal and dual residuals are balanced locally by each agent. Their adaptive penalty needs to be reset after several iterations to guarantee convergence, which results in much weakened convergence conditions.
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