Clarke's tangent vectors as tangents to lipschitz continuous curves

Abstract

Each Clarke tangent vector to a closed set in ℝn at a point in the set is shown to be strictly tangent at that point to some Lipschitz continuous curve lying in the set. This result is quite different in nature from current descriptions of the Clarke tangent cone due to Clarke, Hiriart-Urruty, and others. For the case where the Clarke tangent cone is solid, it is shown that most of the tangential approximants in use in the literature coincide.