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Concept# Linear matrix inequality

Summary

In convex optimization, a linear matrix inequality (LMI) is an expression of the form
: \operatorname{LMI}(y):=A_0+y_1A_1+y_2A_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\succeq0 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}.

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