  We first study Clarke's tangent cones at infinity to unbounded subsets of
$\mathbb{R}^n.$ We prove that these cones are closed convex and show a
characterization of their interiors. We then study subgradients at infinity for
extended real value functions on $\mathbb{R}^n$ and derive necessary optimality
conditions at infinity for optimization problems. We also give a number of
rules for the computing of subgradients at infinity and provide some
characterizations of the Lipschitz continuity at infinity for lower
semi-continuous functions.
