An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

Abstract

For inequality constrained minimization problem, we first propose a new exact nonsmooth objective penalty function and then apply a smooth technique to the penalty function to make it smooth. It is shown that any minimizer of the smoothing objective penalty function is an approximated solution of the original problem. Based on this, we develop a solution method for the inequality constrained minimization problem and prove its global convergence. Numerical experiments are provided to show the efficiency of the proposed method.