Abstract: In the general non-balanced directional switching network,there may be communication delays among agents in networks.In light of this,this paper proposed a distributed subgradient optimization algorithm with communication delays for multi-agent switched networks.In this method,the unconstrained convex optimization problem with communication delays is converted into the unconstrained convex optimization problem without communication delays by augmenting delay nodes in communication network.The convergence of the multi-agent distributed subgradient optimization algorithm with communication delays is proved by using the non-quadratic Lyapunov function method,as long as the non-balanced directional switching network is periodical strong connectivity and the communication delays are upper bounded.Because the network topology conditions and communication delay are both intensively considered,this algorithm is more general and practical.Finally,a simulation example was given to demonstrate the effectiveness of the proposed algorithm.

Key words: Communication delays, Non-quadratic Lyapunov function, Stochastic matrix, Subgradient method, Switched networks