  When restricted to a subspace, a nonsmooth function can be differentiable. It
is known that for a nonsmooth convex function f and a point x, the Euclidean
space can be decomposed into two subspaces: U, over which a special Lagrangian
can be defined and has nice smooth properties and V, the orthogonal complement
subspace of U. In this paper we generalize the definition of UV-decomposition
and U-Lagrangian to the context of nonconvex functions, specifically that of a
prox-regular function.
