Directional differentiability of the distance function
Sergey Ivanovitch Dudov · Sbornik Mathematics · 1995
Necessary and sufficient conditions are obtained for directional differentiability of the distance function from a point to a set, and the corresponding formula is found for the directional derivative for any set and any norm, provided that the directional differentiability is valid. The results are based on a comparison of the cones of tangent directions and the Bouligand cones of the set at points of the marginal set of the distance function, as well as certain joint characteristics of the set and the norm.