On Smoothing \(l_1\) Exact Penalty Function for Nonlinear Constrained Optimization Problems

The penalty function method is a significant method for solving nonlinear constrained optimization problems (COP). In this paper, a new quadratic continuous differentiable smooth penalty function is proposed for the \(l_1\) $l_1$ exact penalty function. The error estimations between the objective function values of the smooth penalty problem, the penalty problem and the original problem are also studied. Furthermore, based on the smoothed penalty function, an algorithm for solving COP is proposed, and the convergence of the algorithm is proved. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.