Distributed Event-Triggered Nonconvex Optimization under Polyak-Łojasiewicz Condition

This paper considers the distributed nonconvex optimization problem, where the goal is to minimize the average of local nonconvex cost functions through local information exchange. Firstly, we propose a distributed optimization algorithm that integrates the gradient tracking method with a dynamic event-triggered communication scheme, thereby reducing communication overhead. Secondly, we demonstrate that the algorithm linearly converges to the global optimum under the Polyak-Łojasiewicz condition, which indicates that every stationary point is a global minimizer. The numerical experiment is presented to validate the theoretical results and confirm the algorithm's effectiveness.