A new neural network for solving nonlinear projection equations

Abstract

This paper proposes a new recurrent neural network for solving nonlinear projection equations. The proposed neural network has a one-layer structure and is suitable for parallel implementation. The proposed neural network is guaranteed to be globally convergent to an exact solution under mild conditions of the underlying nonlinear mapping. Compared with existing neural networks for nonlinear optimization, the asymptotical stability and exponential stability of the the proposed network are obtained without the smooth condition of the nonlinear mapping. The proposed neural network can be used to find the equilibrium point of both the projection neural network and Hopfield-type neural network. Therefore, the proposed neural network is a good solver for a wider class of optimization and related problems. Illustrative examples further show that the proposed neural network can obtain a more accurate solution with a faster convergence rate than existing relevant methods.