A distributed Newton–Raphson-based coordination algorithm for multi-agent optimization with discrete-time communication

This paper proposes a novel distributed continuous-time Newton–Raphson algorithm for distributed convex optimization problem, where the components of the goal are obtainable at different agents. To accelerate convergence speed, we focus on introducing Newton descent idea in our algorithm and extending it in a distributed setting. It is proved that the proposed algorithm can converge to the global optimal point with exponential convergence rate under weight-balanced directed graphs. Motivated by practical considerations, an event-triggered broadcasting strategy is further developed for each agent. Therein, the implementation of communication is driven by the designed triggered condition monitored by agents. Consequently, the proposed continuous-time algorithm can be executed with discrete-time communication, thus being able to greatly save communication expenditure. Moreover, the strategy is proved to be free of Zeno behavior. Eventually, the simulation results illustrate the advantages of the proposed algorithm.