A Smoothing Method of the Square-root Exact Penalty Function for Inequality Constrained Optimization

In order to solve the nonlinear programming problem with inequality constraints, a method for smoothing the square-root exact penalty function is proposed. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth exact penalty problem and of the original constrained optimization problem. Based on the smoothed penalty function, an efficient algorithm for solving the optimization problem with inequality constraints is presented. Moreover, the convergence of the algorithm is proved.