A recurrent neural network for solving nonlinear projection equations

In this paper, we are concerned with the nonlinear projection equations of the following form P_χ(u-F(u))=u. Despite the particular structure of the feasible set χ, the problem is still a very general problem in mathematics programming. Moreover, there are a number of important applications which lead to this special class of variational inequalities such as equilibrium models arising in fields of economics and transportation science, etc. Various numerical solution procedures for the problem have been investigated over decades. Because of the nature of digital computers, conventional algorithms are time-consuming for large-scale optimization problems. It is well-known that one promising approach to optimization problems in real time is to employ artificial neural networks implemented in hardware. Recurrent neural networks for solving optimization problems are readily hardware-implementable. Thus, neural networks are a top choice of real-time solvers for optimization problems. Since the seminal work of Hopfield and Tank (1985), the neural network approach to optimization has been investigated and many neural networks for optimization problems have been proposed