Distributed Dual Decomposition Method with Self-Triggered Communication

In this paper, we consider a distributed method for constrained optimization problems that incorporates self-triggered communication. Each agent cooperatively searches for an optimal solution by exchanging estimates over a communication network among agents. Local communications are sporadically conducted to ensure that the error between the current and last triggered estimates is within a predefined threshold. The next trigger time is computed at the current trigger time in a self-triggered manner. After the information exchange, the estimate is iteratively updated by a consensus-based dual decomposition algorithm. We show that the dual estimates of agents asymptotically converge to an optimal solution under a diminishing and summable stepsize condition. Simulation results show that the proposed self-triggered algorithm can reduce the overall number of communications compared to time-triggered approaches.