Given a subset 
and a point 
, the contingent cone 
at 
with respect to 
is defined to be the set
 |
where 
is the upper left Dini derivative of
the distance function
 |
A classical result in convex analysis characterizes 
as the collection of vectors 
in 
for which there are sequences 
in 
and 
in 
such that 
lies in 
for all 
(Borwein). Intuitively, then, the contingent cone 
consists of limits of directions
to points near 
in 
.
