Generalized gradients and characterization of epi-Lipschitz sets in Riemannian manifolds

In this paper, a notion of generalized gradient on Riemannian manifolds is considered and a subdifferential calculus related to this subdifferential is presented. A characterization of the tangent cone to a nonempty subset SS of a Riemannian manifold MM at a point xx is obtained. Then, these results are applied to characterize epi-Lipschitz subsets of complete Riemannian manifolds.