A proof of the Farkas–Minkowski theorem by a tandem method

Takao Fujimoto, B. B. Upeksha P. Perera and Giorgio Giorgi

Metroeconomica, 2018, vol. 69, issue 1, 142-150

Abstract: This note presents a proof of the Farkas–Minkowski theorem. Our proof does not presuppose the closedness of a finitely generated cone, nor employs separation theorems either. Even the concept of linear independence or invertibility of matrices is not necessary. Our new device consists in proving the Farkas–Minkowski theorem and the closedness of a finitely generated cone at the same time based upon mathematical induction. We make use of a minimization problem with an equality constraint, a method familiar to economics students.

Date: 2018
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