On Notations for Conic Hulls and Related Considerations on Tangent Cones

We propose two di erent notations for cones generated by a set and for convex cones generated by a set, usually denoted by a same notation. We make some remarks on the Bouligand tangent cone and on the Clarke tangent cone for star-shaped sets and for locally convex sets. We give some applications of these remarks to a di erentiable optimization problem with an abstract constraint.