On transient responses of an ADMM-based distributed multi-agent optimization protocol

This paper is concerned with the transient responses of a distributed multi-agent optimization protocol based on the alternating direction method of multipliers (ADMM). Utilizing a representation of an ADMM-based distributed optimization protocol as a feedback system with a linear dynamical system and a nonlinear relation implied by the subgradient, analysis of the transient responses is provided by investigating the poles of the linear subsystem in accordance with the graph representing the communication between agents and the function to be optimized. Several numerical examples are shown to illustrate the results.