Distributed Nonconvex Event-Triggered Optimization Over Time-Varying Directed Networks

Abstract

Many problems in industrial smart manufacturing, such as process operational optimization and decision-making, can be regarded as distributed nonconvex optimization problems, whose goal is to utilize distributed nodes to cooperatively search for the minimal value of the global objective function. With the consideration of data transmission mode, transmission condition, and communication waste in industrial applications, it is meaningful to study the distributed nonconvex optimization problem with an event-triggered strategy over time-varying directed networks. To solve such a problem, a distributed nonconvex event-triggered algorithm is proposed in this article. Under some assumptions on local objective functions, gradients, and step sizes, the convergence of the proposed event-triggered algorithm to the local minimum is established theoretically. Moreover, it is obtained that the proposed distributed event-triggered algorithm has a convergence rate of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(1/\ln (t))$</tex-math></inline-formula> . Finally, two examples of industrial systems are provided to validate the effectiveness of the proposed algorithm.