Sufficiency of Exact Penalty Minimization

By employing a recently obtained error bound for differentiable convex inequalities, it is shown that, under appropriate constraint qualifications, a minimum solution of an exact penalty function for a single value of the penalty parameter which exceeds a certain threshold, is also a solution of the convex program associated with the penalty function. No a priori assumption is made regarding the solvability of the convex program. If such a solvability assumption is made, then we show that a threshold value of the penalty parameter can be used which is smaller than both the above-mentioned value and that of Zangwill. These various threshold values of the penalty parameter also apply to the well-known big-M method of linear programming.