A neural network based on the generalized Fischer–Burmeister function for nonlinear complementarity problems

In this paper, we consider a neural network model for solving the nonlinear complementarity problem (NCP). The neural network is derived from an equivalent unconstrained minimization reformulation of the NCP, which is based on the generalized Fischer–Burmeister function ϕp(a,b)=‖(a,b)‖p-(a+b)ϕp(a,b)=‖(a,b)‖p-(a+b). We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability as well as exponential stability. It was found that a larger p leads to a better convergence rate of the trajectory. Numerical simulations verify the obtained theoretical results.