### From Glossary

The function
is coercive with respect to
if there exists a vector such that for any
sequence having the property that
, we also have

where any norm can be used. This arises in

variational inequalities
(and

complementarity problems).

Some people use a different definition, where
(i.e., a scalar, real-valued function):

Note that the two definitions differ, even for

. For example,

is coercive under the first definition and is not under the second. For the bilinear function,

, for some square matrix

,

is coercive if
there exists

such that