A recurrent neural network for solving variational inequality problems with nonlinear constraints

Variational inequalities with nonlinear inequality constraints are widely used in optimization and engineering problems. This paper present a recurrent neural network for solving variational inequalities with nonlinear inequality constraints in real time. The proposed neural network has one-layer structure and is amenable to parallel implementation. The proposed neural network is a significant generalization of several existing neural networks for optimization. Moreover, the proposed neural network is stable in the sense of Lyapunov and globally convergent to an optimal solution under a strictly monotone condition of the mapping. The simulation shows that the proposed neural network is effective for solving this class of variational inequality problems.