Abstract: In this paper, we propose a method to smooth the general lower order exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. It is shown that under mild assumption, an approximate global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem. We develop an algorithm for solving the original optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. Some numerical examples are given to illustrate the applicability of the present smoothing method.

Key words: constrained nonlinear programming ,  exact penalty function, lower order penalty function, smooth exact penalty function,  second order sufficient condition