Decrease of the Penalty Parameter in the Differentiable Penalty Function Methods

We propose a simple modification to the differentiable penalty methods for solving nonlinear programming problems. This modification decreases the penalty parameter and the illconditioning of the penalty method and leads to a faster convergence to the optimal solution. We extend the modification to the augmented Lagrangian method and report some numerical results on several nonlinear programming test problems, showing the effectiveness of the proposed approach.