Event-triggered zero-gradient-sum distributed consensus optimization over directed networks

This paper focuses on the event-triggered zero-gradient-sum algorithms for a distributed convex optimization problem over directed networks. The communication process is driven by trigger conditions monitored by nodes. The proposed trigger conditions are decentralized and just depend on each node’s own state. In the continuous-time case, we propose an algorithm based on a sample-based monitoring scheme. In the discrete-time case, we propose a new event-triggered zero-gradient-sum algorithm which is suitable for more general network models. It is proved that two proposed event-triggered algorithms are exponentially convergent if the design parameters are chosen properly and the network topology is strongly connected and weight-balanced. Finally, we illustrate the advantages of the proposed algorithms by numerical simulation.