Edge-based event-triggered distributed inexact gradient descent for convex optimization

This paper investigates an event-triggered (ET) distributed convex optimization (DCO) over a multi-agent network. To save network resources to some extent, an edge-based event-triggered (EBET) scheme is introduced. Then an edge-based event-triggered distributed inexact gradient descent (EBET-DIGD) algorithm is developed. Under the developed algorithm, we prove that the individual state of each node asymptotically converges to the optimal solution in the presence of choosing the suitable EBET condition. Meanwhile, we analyze the convergence of the proposed algorithm as well, and the convergence rate in regard to the time-averaged state of each agent is provided. In the end, a simulation example is presented to validate the developed algorithm.