HADAMARD AND STRONG WELL-POSEDNESS FOR CONVEX-PROGRAMS

It is proved that Hadamard well-posedness of a constrained convex opti mization problem with respect to Attouch-Wets convergence on the data implies, in general, its strong (and hence Tykhonov) well-posedness. A n example is given showing that the opposite implication fails without assuming an appropriate constrained qualification condition.