LOCAL SOLUTIONS OF CONSTRAINED MINIMIZATION PROBLEMS AND CRITICAL POINTS OF LIPSCHITZ FUNCTIONS

Abstract

In this paper we use the penalty approach in order to study two constrained nonconvex minimization problems with locally Lipschitzian objective and constraint functions in a Banach space. We show that a local minimizer of the constrained minimization problem which is not a critical point of the constraint function is also a local minimizer of a corresponding unconstrained penalized problem if a penalty coefficient is large enough.