Solving nonlinear complementarity problems with neural networks: a reformulation method approach

In this paper, we present a neural network approach for solving nonlinear complementarity problems. The neural network model is derived from an unconstrained minimization reformulation of the complementarity problem. The existence and the convergence of the trajectory of the neural network are addressed in detail. In addition, we also explore the stability properties, such as the stability in the sense of Lyapunov, the asymptotic stability and the exponential stability, for the neural network model. The theory developed here is also valid for neural network models derived from a number of reformulation methods for nonlinear complementarity problems. Simulation results are also reported.