A Simplified Recurrent Neural Network for Solving Nonlinear Variational Inequalities

A recurrent neural network is proposed to deal with the nonlinear variational inequalities with linear equality and nonlinear inequality constraints. By exploiting the equality constraints, the original variational inequality problem can be transformed into a simplified one with only inequality constraints. Therefore, by solving this simplified problem, the neural network architecture complexity is reduced dramatically. In addition, the proposed neural network can also be applied to the constrained optimization problems, and it is proved that the convex condition on the objective function of the optimization problem can be relaxed. Finally, the satisfactory performance of the proposed approach is demonstrated by simulation examples.