Distributed multi-agent optimization via event-triggered based continuous-time Newton–Raphson algorithm

Abstract

Abstract This paper investigates the problem of distributed convex optimization for multi-agent networks, where the objective function is the summation of local and multidimensional cost functions associated to private agents. To begin with, we develop a continuous-time Newton–Raphson algorithm, which features reduced communication, fast convergence and distributed execution, to solve such a problem. To avoid continuous control signal updating, an asynchronous event-triggered scheme is proposed for each agent. As a consequence, the continuous-time Newton–Raphson can be implemented with discrete-time control law driven by our designed trigger conditions, which is more suitable for practical applications. In addition, the triggering instants for each agent are not influenced by its neighboring agents’ latest triggering instants, resulting in reduced total triggering events. It is proved that each agent can exponentially converge to the global optimal point by implementing the proposed algorithms and the proposed event-triggered scheme is naturally free of Zeno behavior. Several examples illustrate our results.