A gradient-based dissipative continuous-time algorithm for distributed optimization

This paper is concerned with solving distributed optimization problem by multi-agent systems with gradient-based dissipative dynamics over undirected graph. The optimization objective function is a sum of local cost functions associated to the individual agents. A novel gradient-based dissipative continuous-time algorithm is proposed to solve the distributed optimization problem, which extends the well-known heavy ball method to distributed optimization. Suppose the local cost functions being strongly convex with locally Lipschitz gradients, by defining suitable Lyapunov functions, then we show that the agents can find the same optimal solution by the proposed algorithm with exponential convergence rate. Specially, the choice of parameters in our algorithm is independent of the communication topology, demonstrating significant advantage over existing algorithms.