In this paper, a new smoothing approximation to the k-th
power nonlinear penalty function for constrained optimization problems is
presented. We prove that this type of the smoothing penalty functions has good
properties in solving constrained optimization problems. Furthermore, based on
the smoothed penalty problem, an algorithm is presented to solve the
constrained optimization problems, with its convergence under some conditions
proved. Some numerical examples are given to illustrate the applicability of
the present smoothing method, which show that the algorithm seems efficient.