The set of all subgradients at "x"0 is called the subdifferential at "x"0 and is denoted ∂"f"("x"0). The subdifferential is always a nonempty convex compact set. These concepts generalize further to convex functions "f":"U"→ R on a convex set in a locally convex space "V". A functional formula_16∗ in the dual space V∗ is called "subgradient" at "x"0 in "U" if for all "x" in "U" The set of all subgradients at "x"0 is called the subdifferential at "x"0 and is again denoted ∂"f"("x"0). The subdifferential is always a convex closed set. It can be an empty set; consider for example an unbounded operator, which is convex, but has no subgradient. If "f" is continuous, the subdifferential is nonempty. The subdifferential on convex functions was introduced by Jean Jacques Moreau and R. Tyrrell Rockafellar in the early 1960s. The "generalized subdifferential" for nonconvex functions was introduced by F.H. Clarke and R.T. Rockafellar in the early 1980s.