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
.