On Partial Smoothness, Tilt Stability and the   $\mathcal{VU}$--Decomposition
  Under the assumption of prox-regularity and the presence of a tilt stable local minimum we are able to show that a $\mathcal{VU}$ like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function. 
Andrew Eberhard, Yousong Luo and Shuai Liu
math.OC