Distributed Event-Triggered Subgradient Method for Convex Optimization with a Common Constraint Set

Abstract This paper proposes a discrete-time event-triggered subgradient algorithm to minimize a sum of local cost functions under a common constraint set. In the proposed method, each agent sends its state to a neighbor agent based on the edge-based event-triggering mechanism. We consider a consensus-based subgradient algorithm with a projection to the constraint set so that states of all agents asymptotically converge to an optimal solution. Simulation results confirm that the proposed event-triggered subgradient algorithm can effectively reduce the number of communications compared with the time-triggered algorithm.