Design of Event-Triggered Distributed Optimization Algorithms over Directed Graphs

This paper investigates the event-triggered distributed optimization problem over directed graphs. Based on the event-triggered communication over directed graphs, the purpose of this paper is to design a group of distributed optimization algorithms and to reduce the cost of communication. Firstly, by introducing an event-triggered estimator, one can asymptotically estimate the left eigenvector corresponding to the zero eigenvalue of the network Laplace matrix. Then, by embedding the proposed event-triggered estimator to the designed event-triggered distributed optimization algorithms, the sum of convex objective functions is minimized. Finally, it is also proved that the system is free of Zeno behavior and singularity of the designed event-triggered distributed optimization algorithms. Compared with the existing distributed optimization results, the main contributions of this paper are that 1) the communication graphs are directed, 2) the communication mode is event-triggered scheme. Both from communication graph and mode, the cost of communication will be reduced. To the best of our knowledge, this is the first study of event-triggered distributed optimization over weighted-unbalanced directed graphs. Finally, a simulation example is presented to illustrate the effectiveness of distributed event-triggered optimization algorithms.