Smoothing Approximation to the New Exact Penalty Function with Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.