Distributed Nonconvex Optimization With Event-Triggered Communication

This article considers distributed nonconvex optimization for minimizing the sum of local cost functions by using local information exchange. In order to avoid continuous communication among agents and reduce communication overheads, we develop a distributed algorithm with a dynamic exponentially decaying event-triggered scheme. We show that the proposed algorithm is free of Zeno behavior (i.e., finite number of triggers in any finite time interval) by contradiction and asymptotically converges to a stationary point if the local cost functions are smooth. Moreover, we show that the proposed algorithm exponentially converges to the global optimal point if, in addition, the global cost function satisfies the Polyak–Łojasiewicz condition, which is weaker than the standard strong convexity condition, and the global minimizer is not necessarily unique. The theoretical results are illustrated by a numerical simulation example.