Distributed dynamic optimization over directed graphs

This paper considers distributed convex optimization problems over a multi-agent network, with each agent possessing a dynamic objective function. The agents aim to collectively track the minimum of the sum of locally known time-varying convex functions by exchanging information between the neighbors. We focus on scenarios when the communication among the agents is described by a directed network. We devise an algorithm with a discrete time-sampling scheme such that the distance between any agent estimate and time-varying optimal solutions converges to a steady state error bound whose size is related to the constant step-size and the sampling interval. The convergence rate is shown to be linear given that the objective function is strongly-convex. Numerical simulations demonstrate the practical utility of the proposed approach.