Distributed Optimization With Asynchronous Computation and Event-Triggered Communication

The implementation of distributed optimization, depending on the application, imposes escalating demands on communication and computational synchronization, with the general desire for the robust performance in the face of computationally slow agents and the avoidance of unnecessary communication. In this article, we propose a distributed algorithm with asynchronous computation and event-triggered communication (DAAET) that enables the nodes to flexibly determine their update and information transmission instants. DAAET achieves compatibility with nodes operating at varying computation frequencies and accomplishes a reduction in both wall time and communication costs. Meanwhile, this article proposes a model reconstruction technique to handle disconnectivity arising from the asynchronous implementation of the event-triggered mechanism. Theoretical analysis demonstrates the algorithm's linear convergence to the global optimum under relaxed conditions. The effectiveness and advantages of our approach are demonstrated through a set of examples, showcasing its potential for practical applications.