A new neural network based on smooth function for SOCCVI problems

A new neural network is proposed to solve the second-order cone constrained variational inequality (SOCCVI) problems. Instead of the smoothed Fishcer-Burmeister function, a smooth regularized Chen-Harker-Kanzow-Smale (CHKS) function is used to handle relevant complementarity conditions. By using a neural network approach based on the CHKS function, the KKT conditions corresponding to the SOCCVI are solved. Some stability properties of the neural network can be verified by the Lyapunov method. When the parameters of the neural network are different, the achieved convergence speed will also vary. Further by controlling the corresponding parameters, the neural network can achieve a faster convergence speed than a classical model. Numerical simulations are applied to examine the computing capability of the neural network as well as the influence of parameters on it.