Farkas’ Lemma Derived by Elementary Linear Algebra
نویسنده
چکیده
This note presents a partially new proof of Farkas’ lemma, based on no other tools than elementary linear algebra (matrixand vector calculus). No properties of the real numbers other than those shared by the rational numbers are used. The general approach is the same as in the paper by A. Dax from 1997 (SIAM Review, 39(3):503-507), but instead of using an active set method for proving the existence of optimal solutions to sign-constrained linear least squares problems (the hard part of the proof), we use a natural partitioning of the feasible region into disjunct subregions, followed by a simple investigation of each subregion.
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