A Short Algebraic Proof of the Farkas Lemma
David Bartl · SIAM Journal on Optimization · 2008
The purpose of this paper is to present a generalization of the Farkas lemma with a short algebraic proof. The generalization lies in the fact that we formulate the Farkas lemma in the setting of two vector spaces over a common linearly ordered field where one of the vector spaces is also linearly ordered. At the end of the paper, we mention the key theorem and two theorems of the alternative, namely Motzkin's theorem and Tucker's theorem.