Accelerated Gradient Flow for Directed Graphs with Event-Based Broadcasting

Accelerated gradients algorithms are currently at the receiving end of widespread interest in optimization theory, both under discrete-and continuous-Time (CT) frameworks. In light of recent developments, in the first part of our work, we design a CT accelerated gradient algorithm for strongly connected directed graphs. We show that the convergence is exponential and the convergence rate is proportional to the gradient gain which is chosen arbitrarily. To facilitate implementation of the algorithm over communication networks, in the second part of our work, we design an event-based broadcasting protocol that intermittently checks for events by evaluating an event-Triggering condition and accordingly makes decision on broadcasting. The distributed system, with CT dynamics and discrete-Time (event-based) broadcasts, is reformulated as a hybrid dynamical system which is devoid of Zeno solutions. Finally, we provide a numerical example to demonstrate our results.