STABILITY OF EXACT PENALTY FOR NONCONVEX INEQUALITY-CONSTRAINED MINIMIZATION PROBLEMS

Abstract

In this paper we use the penalty approach in order to study inequality-constrained minimization problems with locally Lipschitz objective and constraint functions 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 objective functions, constraint functions and the right-hand side of constraints.