Cooperative convex optimization with subgradient delays using push-sum distributed dual averaging

Abstract In this paper, we address the distributed convex optimization problems for multi-agent systems. In our research, it is assumed that each agent in the multi-agent system could merely interact with its neighbors via a directed graph and is available to its own cost function. We then utilize the push-sum distributed dual averaging (PS-DDA) algorithm to tackle with the distributed optimization problem. However, we consider that there exist subgradient delays in PS-DDA algorithm. The proof of the main result which shows that the PS-DDA algorithm with subgradient delays converges and the error possesses sublinear growth of a rate O ( τ 2 T − 0.5 ) , where T denotes the total amount of iterations, is detailed presented in this paper. Finally, a numerical example is simulated to show the performance of the algorithm we study in this paper.