An initialization-free continuous-time distributed algorithm for convex optimization problem

In this paper, a distributed convex optimization problem for continuous-time multi-agent systems is studied. The objective function is equal to the sum of several strongly convex cost functions with Lipschitz gradients, which are solved by the corresponding agents. A new distributed algorithm is proposed and the multi-agent system is represented by a strongly connected undirected graph. The exponential convergence of the algorithm is analyzed and the minimum exponential convergence rate is obtained. Finally, mathematical simulations are implemented to illustrate the results.