Abstract
This paper discusses the distributed optimization problem for the continuous-time and discrete-time multi-agent systems. For such a problem, each agent possesses a local convex cost function only known by itself and all the agents converge to the optimizer of the sum of the local cost function through estimating the optimal states of the local cost function and exchanging states information between agents. Sufficient conditions for convergence to the optimizer of the continuous-time and discrete-time algorithms are provided by making use of the Lyapunov method. We also obtain the least convergence rate for the modified algorithm. Moreover, numerical simulations are supplied to testify the results we present. (C) 2017 Elsevier B.V. All rights reserved.