A Neural Network Approach for Solving Weighted Nonlinear Complementarity Problems

In this paper, we consider the weighted nonlinear complementarity problem which is the extension of the general complementarity problems and contains a wide class of optimization problems. Based on the weighted complementarity function, we reformulate the weighted nonlinear complementarity problem as an unconstrained minimization problem and present the steepest descent-based neural network to solve it. Under mild conditions, we derive some results related to the asymptotic stability of the neural network. Numerical experiments indicate that the proposed algorithm is quite effective.