# Complementary slackness

### From Glossary

The condition that two non-negative vectors
are orthogonal. It
arises in the Kuhn-Tucker conditions,
where the Lagrange multiplier, say , must
be orthogonal to the (inequality) constraint functional value:
. This means either
or for each -- that
is, if a constraint is not active, its Lagrange multiplier
must be zero.