Push-sum Distributed Dual Averaging for Convex Optimization in Multi-agent Systems with Communication Delays

The distributed convex optimization problem over the multi-agent system is considered in this paper, and it is assumed that each agent possesses its own cost function and communicates with its neighbours over a sequence of timevarying directed graphs. However, due to some reasons there exist communication delays while agents receive information from other agents, and we are going to seek the optimal value of the sum of agents’ loss functions in this case. We desire to handle this problem with the push-sum distributed dual averaging (PSDDA) algorithm which is introduced in [22]. It is proved that this algorithm converges and the error decays at a rate O (

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