Farkas' Lemma

Farkas' Lemma

Farkas's lemma is a result in mathematics stating that a vector is either in a given convex cone or that there exists a (hyper)plane separating the vector from the cone - there are no other possibilities. It was originally proved by the Hungarian mathematician Gyula Farkas (1894, 1902). It is used amongst other things in the proof of the Karush–Kuhn–Tucker theorem in nonlinear programming.

Farkas's lemma is an example of a theorem of the alternative; a theorem stating that of two systems, one or the other has a solution, but not both or none.