A NEURAL NETWORK FOR THE GENERALIZED NONLINEAR COMPLEMENTARITY PROBLEM OVER A POLYHEDRAL CONE

Abstract

In this paper, we consider a neural network model for solving the generalized nonlinear complementarity problem (denoted by GNCP) over a polyhedral cone. The neural network is derived from an equivalent unconstrained minimization reformulation of the GNCP, which is based on the penalized Fischer–Burmeister function ${\it\phi}_{{\it\mu}}(a,b)={\it\mu}{\it\phi}_{\mathit{FB}}(a,b)+(1-{\it\mu})a_{+}b_{+}$. We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability and exponential stability. It is found that a larger ${\it\mu}$ leads to a better convergence rate of the trajectory. Simulation results are also reported.