A passivity-based perspective for distributed optimization and integration of communication delays

In this paper, we present a perspective that a solution process for a class of distributed optimization is passive. After formulating the intended distributed optimization problem, we design a distributed optimization dynamics based on so-called PI consensus algorithm. The dynamical system is then shown to be regarded as a feedback interconnection of passive systems and hence to preserve passivity. As a benefit of the passivity-based perspective, we then integrate interagent communication delays using passivity-based output synchronization techniques together with so-called scattering transformation.