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algebra > elementary algebra > inequality > linear matrix inequality

optimization > linear matrix inequality

Preferred term

linear matrix inequality

Definition(s)

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

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

where
- ${\\displaystyle y=[y_{i}\\,,~i\\!=\\!1,\\dots ,m]}$ is a real vector,
- ${\\displaystyle A_{0},A_{1},A_{2},\\dots ,A_{m}}$ are ${\\displaystyle n\ imes n}$ symmetric matrices ${\\displaystyle \\mathbb {S} ^{n}}$ ,
- ${\\displaystyle B\\succeq 0}$ is a generalized inequality meaning ${\\displaystyle B}$ is a positive semidefinite matrix belonging to the positive semidefinite cone ${\\displaystyle \\mathbb {S} _{+}}$ in the subspace of symmetric matrices ${\\displaystyle \\mathbb {S} }$ .
This linear matrix inequality specifies a convex constraint on y.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Linear_matrix_inequality)

Broader concept(s)

In other languages

inégalité matricielle linéaire

French

URI

http://data.loterre.fr/ark:/67375/PSR-RXNJS1M1-N

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