Smoothing approximation to l1l1 exact penalty function for inequality constrained optimization

In this paper, we propose a method to smooth l1l1 exact penalty function for inequality constrained optimization. It is shown that an approximate global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem. Under some mild conditions, the method based on our smoothing function is shown to be globally convergent. Some numerical examples are given to illustrate the applicability of the present smoothing method.