Abstract
The theorem of this paper is of the same general class as Farkas' Lemma, Stiemke's Theorem, and the Kuhn—Fourier Theorem in the theory of linear inequalities. LetV be a vector subspace ofR n, and let intervalsI 1,⋯, I n of real numbers be prescribed. A necessary and sufficient condition is given for existence of a vector (x 1,⋯, x n) inV such thatx i ∈I i (i = 1, ⋯,n); this condition involves the “elementary vectors” (nonzero vectors with minimal support) ofV ⊥. The proof of the theorem uses only elementary linear algebra.
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The author at present holds a Senior Scientist Award of the Alexander von Humboldt Stiftung.
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Minty, G.J. A “from scratch” proof of a theorem of Rockafellar and Fulkerson. Mathematical Programming 7, 368–375 (1974). https://doi.org/10.1007/BF01585531
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DOI: https://doi.org/10.1007/BF01585531