# Subdifferential

### From Glossary

(of at ). Also see conjugate function. If is convex and differentiable with gradient,

The subdiffenential is built on the concept of supporting hyperplane, generally used in convex analysis. When is differentiable in a deleted neighborhood of (but not necessarily at ), the *B-subdifferential* is the set of limit points:

If is continuously differentiable in a neighborhood of (including ),
Otherwise,
is generally not a convex set. For example, if

The ** Clarke subdifferential** is the convex hull of