Existence of exact penalty for optimization problems with mixed constraints in Banach spaces

In this paper we use the penalty approach in order to study constrained minimization problems in a Banach space with nonsmooth nonconvex mixed constraints. A penalty function is said to have the exact penalty property [J.-B. Hiriart-Urruty, C. Lemarechal, Convex Analysis and Minimization Algorithms, Springer, Berlin, 1993] if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper we establish sufficient conditions for the exact penalty property.