Farkas' lemma (Q606254)

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theorem

Language	Label	Description	Also known as
English	Farkas' lemma	theorem

Statements

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linear programming

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defining formula

{\begin{aligned}\forall A\in &\mathbb {R} ^{m\times n},\forall \mathbf {b} \in \mathbb {R} ^{n},{\text{exactly one of the following is true:}}\\&{\begin{aligned}&\exists \mathbf {x} \in \mathbb {R} ^{n}:\mathbf {Ax} =\mathbf {b} \wedge \mathbf {x} \geq 0\\&\exists \mathbf {y} \in \mathbb {R} ^{m}:\mathbf {A} ^{\top }\mathbf {y} \geq 0\wedge \mathbf {b} ^{\top }\mathbf {y} <0\end{aligned}}\end{aligned}}

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

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Freebase Data Dumps

publication date

28 October 2013

Microsoft Academic ID

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Sitelinks

Wikipedia(10 entries)

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Wikiversity(0 entries)

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Wiktionary(0 entries)

Multilingual sites(0 entries)

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