A Method to Overcome the Ill-Conditioning Problem of Differentiable Penalty Functions

In recent years there has been considerable interest in the method of modified Lagrangian to solve the nonlinear programming problem. The main reason is that the modified Lagrangian approach overcomes the ill-conditioning problem and the slow convergence of the penalty methods. The purpose of this paper is to present a simple modification to the existing differentiable penalty functions for solving the nonlinear programming problem. This modification overcomes the ill-conditioning problem resulting from the controlling parameter being either too small or too large. Numerical experience is also presented.