Stability Analysis of Distributed Scheduling using ADMM and Proposal of a Modified Algorithm

In recent years, the development of optimization methods in multi-agent systems has been remarkable. We have proposed a distributed scheduling method using the Alternating Direction Method of Multipliers (ADMM). However, in many cases, the scheduling process oscillates and does not converge. In this study, we present a theorem regarding the stability of distributed scheduling using ADMM. Additionally, we propose a modified ADMM algorithm to ensure that the algorithm reaches a stable state. The results of computer experiments demonstrate the effectiveness of the proposed method.