Dynamical Analysis of Neural Networks of Subgradient System

In this technical note, we consider a class of neural network, which is a generalization of neural network models considered in the optimization context. Under some mild assumptions, this neural network can be translated into a negative subgradient dynamical system. At first, we study the existence and uniqueness of solution of this neural network. Then, by nonsmooth Łojasiewicz inequality, we prove the convergence of the trajectories of this neural network. In the end, a constrained minimization problem is studied, which can be associated with this neural network. It is proved that the local constrained minimum of the cost function coincides with the stable equilibria point of this neural network.