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Farkas' lemma

Farkas' lemma is a solvability theorem for a finite system of linear inequalities in mathematics. It was originally proven by the Hungarian mathematician Gyula Farkas. Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively, mathematical programming). It is used amongst other things in the proof of the Karush–Kuhn–Tucker theorem in nonlinear programming. Remarkably, in the area of the foundations of quantum theory, the lemma also underlies the complete set of Bell inequalities in the form of necessary and sufficient conditions for the existence of a local hidden-variable theory, given data from any specific set of measurements.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Farkas%27_lemma)

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