Solving Nonlinear Complementarity Problems with Linear Threshold Neural Networks

In this paper, we present a recurrent neural network for solving the nonlinear complementarity problems. The neural network model is derived from an unconstrained reformulation of the nonlinear complementarity problems. It is proved that the trajectories are still in R⁺ with the initial state in R⁺. The existence of the equilibrium points of the linear threshold neural networks is addressed in this paper. In addition, the convergence of the trajectory of the LT neural network is studied in this paper. Simulation shows that the proposed network is effective in solving these nonlinear complementarity problems.