Show that T(x*) ⊂ L(x*).
The Kuhn-Tucker first-order conditions are necessary for a local optimum at x* provided that the linearizing cone L(x*) is equal to the cone of tangents T(x*), which is known as the Abadie constraint qualification condition. The Kuhn-Tucker conditions follow immediately from proposition 5.3 by a straightforward application of the Farkas lemma.