The contingent cone 
at a point 
of a subset 
is the set
 |
(1)
|
where 
is the lower right directional Dini derivative
 |
(2)
|
and 
is the distance function
 |
(3)
|
A classical result in convex analysis characterizes 
as the collection of vectors 
in 
for which there are sequences 
of positive
real numbers and 
in 
such that 
lies in 
for all 
(Borwein and Lewis 2006, p. 138). Intuitively, the contingent
cone 
consists of limits of directions
to points near 
in 
.
