Existence of Exact Penalty and its Stability for Inequality-Constrained Optimization Problems

We use the penalty approach in order to study a large class of inequality-constrained minimization problems in Banach spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. In this paper we show that the generalized exact penalty property is stable under perturbations of cost functions, constraint functions and the right-hand side of constraints.