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.