LMI meaning in Maths ?

Answer:

What is Linear Matrix Inequality mean?

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

LMI ⁡ ( y ) := A 0 + y 1 A 1 + y 2 A 2 + ⋯ + y m A m ⪰ 0 {\displaystyle \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 , … , m ] {\displaystyle y=[y_{i}\,,~i\!=\!1,\dots ,m]} is a real vector, A 0 , A 1 , A 2 , … , A m {\displaystyle A_{0},A_{1},A_{2},\dots ,A_{m}} are n × n {\displaystyle n\times n} symmetric matrices S n {\displaystyle \mathbb {S} ^{n}} ,reference

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