Solving mathematical programs with vanishing constraints using a gradient-based neural network model

In this paper, a gradient-based neural network model is applied to successfully determine the solution of a class of nonlinear optimization problems known as Mathematical Programs with Vanishing Constraints (MPVC). First, a smoothing and regularization technique is used to transform the original MPVC problem into a smooth and relaxed nonlinear optimization problem. Then, by utilizing the penalty function method and a gradient-based neural network model, the optimal solution of the transformed nonlinear problem is estimated. The proposed model has a straightforward structure and low computing cost. Theoretical investigation of the neural network has shown that the equilibrium of the suggested network is asymptotically stable and converges to the optimal solution of the original MPVC. Simulation results provide additional evidence that supports the theoretical analysis and confirms the computational efficiency of the suggested network.