Linear matrix inequality information

In convex optimization, a linear matrix inequality (LMI) is an expression of the form

\operatorname {LMI} (y):=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\cdots +y_{m}A_{m}\succeq 0\,

where

$y=[y_{i}\,,~i\!=\!1,\dots ,m]$ is a real vector,
$A_{0},A_{1},A_{2},\dots ,A_{m}$ are $n\times n$ symmetric matrices $\mathbb {S} ^{n}$ ,
$B\succeq 0$ is a generalized inequality meaning $B$ is a positive semidefinite matrix belonging to the positive semidefinite cone $\mathbb {S} _{+}$ in the subspace of symmetric matrices $\mathbb {S}$ .

This linear matrix inequality specifies a convex constraint on $y$ .

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