Based on the multi-agent system model over switching network with random communication delay, we propose a distributed multi-step subgradient random projection algorithm and analyze the convergence and convergence rate of the proposed algorithm. The multi-step subgradient of agents is a combination of the subgradient at current time and all the historical subgradient. Batch random projection is utilized in proposed algorithm to improve the accuracy of random projection. To simplify the process of convergence analysis we propose a method of system expansion to replace the random communication delay. The final numerical simulation results show that the multi-step subgradient random projection algorithm has a faster convergence speed than the traditional subgradient algorithm.
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