Mathematical convex optimization
In convex optimization, a linear matrix inequality (LMI) is an expression of the form
![{\displaystyle \operatorname {LMI} (y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\cdots +y_{m}A_{m}\succeq 0\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9146e5a3c0820b3321a9624832c9724496582f15)
where
is a real vector,
are
symmetric matrices
,
is a generalized inequality meaning
is a positive semidefinite matrix belonging to the positive semidefinite cone
in the subspace of symmetric matrices
.
This linear matrix inequality specifies a convex constraint on
.