On Partial Smoothness, Tilt Stability and the $\mathcal{V}\mathcal{U}$--Decomposition

Abstract

Under the assumption of prox-regularity and the presence of a tilt stable local minimum we are able to show that a $\mathcal{V}\mathcal{U}$ like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function.

28 pages