A nonautonomous-differential-inclusion neurodynamic approach for nonsmooth distributed optimization on multi-agent systems

This paper considers a category of nonsmooth distributed optimization on multi-agent systems, where agents own privacies and collectively minimize a sum of local cost functions. Taking the restrictions on communication among agents into consideration, a nonautonomous-differential-inclusion neurodynamic approach is proposed over a weighed topology graph. The convergence of neural network is analyzed and its state exponentially converges to an optimal solution of distributed optimization under certain conditions. Since no additional conditions are required to guarantee the convergence, the neural network is superior to distributed algorithms based on penalty method, which need to estimate penalty parameters. Compared with some existed approaches, the neural network has the advantage of possessing fewer state variables. Finally, illustrative examples and an application in distributed quantile regression are delineated to testify the effectiveness of the presented neural network.