Abstract: In this paper, two function forms of quadratic smoothing approximation to the lower order exact penalty function are proposed to generate modified smooth penalty functions for inequality-constrained optimization problems. It is shown that under certain conditions, any global minimizer of the modified smooth penalty problem is a global minimizer to the original constrained optimization problem when the penalty parameter is sufficiently large. Two numerical examples are given to show the effectiveness of the present smoothing scheme.

Key words:  modified penalty function,  smoothing approximation, lower order penalty function, inequality-constrained optimization problem