History of Mathematics – Who Called Farkas’ Fundamental Theorem a Lemma?

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Farkas proved his famous result (which, nowadays, is fundamental in optimization theory) in 1902 and called it Grundsatz der einfachen Ungleichung which may be translated as fundamental theorem of simple inequalities (where simple means linear, I know that Grundsatz can also be translated as principle, but reading Farkas, I strongly believe that fundamental theorem fits better).

Question. Who was the first to call his fundamental theorem the Farkas' lemma?

I have edited the question because of the comments which concern the former formulation of a relegation.

Best Answer

This is the earliest reference I have located:

Minkowski-Farkas Lemma in Banach Spaces, L. Hurwicz (1952).

The same result was also referred to as the Minkowski-Farkas-Weyl theorem in the 1950's, for example in

The strong Minkowski-Farkas-Weyl theorem for vector spaces over ordered fields, A. Charnes and W.W. Cooper (1958).

The three authors are associated with this result in view of the following contributions:

  • H. Minkowski, Geometrie der Zahlen (Leipzig, 1896).
  • J. Farkas, Über die Theorie der einfachen Ungleichungen, Journal für die reine und angewandte Mathematik, 124, 1-27 (1902).
  • H. Weyl, Elementare Theorie der konvexen Polyeder, Comm. Helvet., 7, 290-306 (1935).
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