A penalty function method based on smoothing lower order penalty function

The paper introduces a smoothing technique for a lower order penalty function for constrained optimization problems (COP). It is proved that the optimal solution to the smoothed penalty optimization problem is a $\frac{ϵ}{2}$ ‐approximate optimal solution to the original optimization problem under some mild assumptions. Based on the smoothed penalty function, an algorithm for solving COP is proposed and some numerical examples are given.