Quadratic smoothing approximation to 1 over 2-order exact penalty function

In this paper, we propose a quadratic smoothing approximation to the 1/2-order exact penalty function. It is shown that when the penalty parameter of the smoothed penalty problem with the smoothing approximation function being penalty function is sufficiently large, any global minimizer of the smoothed penalty problem is an approximate feasible point of the original optimization problem, and the difference between the original objective function value on a global minimizer of the smoothed penalty problem and the global optimal value of the original problem can be controlled by the smoothing parameter which can be set in advance. Two numerical examples are reported to show the effectiveness of the proposed quadratic smoothing approximation method.