Distributed continuous-time optimization in multi-agent networks with undirected topology

Abstract

By using combined tools from smooth approximation technique and exact penalty method, a smooth distributed continuous-time algorithm is designed in this paper to solve a kind of convex problem in multi-agent networks with undirected topology. One of the remarkable features of this paper lies in the fact that a convergence rate $O(1 /t^{2})$ could be yielded by using the proposed distributed algorithm if, some suitable conditions are satisfied. Specifically, by using the smooth approximation method, a kind of distributed algorithm is proposed to deal with the optimization problem with non-smooth cost functions or cost functions having non-Lipschitz gradient. The asymptotic convergence property and the convergence rate of the proposed distributed algorithm are analyzed under certain mild conditions. A numerical simulation is conducted to validate the effectiveness of the theoretical analysis.