Event-triggered asynchronous distributed optimization algorithm with heterogeneous time-varying step-sizes

This paper concerns distributed convex optimization problems over time-varying undirected graphs, in which the global objective function is expressed as the sum of individual objective functions of the agents. Each agent only knows its local objective functions. To figure out such problems, an event-triggered asynchronous distributed optimization algorithm (termed as EV-ADOA) with time-varying heterogeneous step-sizes is proposed, which is suitable for undirected graphs changing over time. Under two standard assumptions on strongly convex and smoothness of local objective functions, the EV-ADOA can achieve linear convergence with a proper upper bound of the heterogeneous time-varying step-sizes. EV-ADOA with event-triggered scheme can decrease network communication, and the Zeno-like behavior strictly is excluded. The efficiency of EV-ADOA is demonstrated by experiments.