# Tangent cone

### From Glossary

Let
and let
The *tangent cone*,
is the set of points that have the following limit properties:
is in
if there exist sequences
such that
This arises in connection with the Lagrange Multiplier Rule much like
the tangent plane, though it allows
for more general constraints – e.g., set constraints. In
particular, when there are only equality constraints,
of
if
has full row rank.
(There are some subtleties that render the tangent cone more
general, in some sense, than the tangent plane or null space. It is
used in establishing a *necessary* constraint qualification.)