In convex optimization, a linear matrix inequality is an expression of the form LMI ⁡ := A 0 + y 1 A 1 + y 2 A 2 + ⋯ + y m A m ⪰ 0 {\displaystyle \operatorname {LMI} :=A_{0}+y_{1}A_{1}+y_{2}A_{2}+\cdots +y_{m}A_{m}\succeq 0\,} where y = [ y i, i = 1, …, m ] {\displaystyle y=[y_{i}\,,~i\! Wikipedia