<p>In this paper, we propose a neural network based on an augmented Lagrangian function to solve a challenging class of constrained optimization problems called Mathematical Programs with Equilibrium Constraints (MPEC). The original MPEC problem, which includes equilibrium constraints, is first transformed into an equivalent nonlinear programming formulation using a smoothing technique. A neural network inspired by the augmented Lagrangian method is then employed to solve the reformulated problem. The proposed approach is rigorously analyzed in terms of stability, convergence, and computational performance, ensuring its effectiveness and reliability. Under specific assumptions, it is demonstrated that the neural network converges to an equilibrium point that satisfies the Karush-Kuhn-Tucker (KKT) conditions of the underlying nonlinear programming problem, guaranteeing the optimality of the obtained solution. The stability of the network is further established through the Lyapunov function method. To validate the approach, several numerical simulations are conducted, and the reported results are compared with the Lagrange Programming Neural Network. The proposed model is also applied to compute Stackelberg-Cournot-Nash equilibria to demonstrate its versatility and practical relevance.</p>