A sufficient condition for exact penalty in constrained optimization

In this paper we use the penalty approach to study three constrained minimization problems. A penalty function is said to have the exact penalty property [J.- B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms, 2 vols., Springer-Verlag, Berlin, 1993] if there exists 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 a very simple sufficient condition for the exact penalty property.