this paper we have given an alternative proof of Farkas's lemma, a proof that is based on a theorem, the main theorem, that relates to the eigenvectors of certain orthogonal matrices. This theorem is believed to be new, and the author is not aware of any similar theorem concerning ...
Bartl, D. A note on the short algebraic proof of Farkas' Lemma. Linear and Multilinear Algebra, 60 (2012) 897-901.Bartl, D. (2012a): `A note on the short algebraic proof of Farkas' Lemma', Linear & Multilinear Algebra, 60, pp. 897-901....
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. Let V be a vector subspace of R n , and let intervals I 1 , , I n of real numbers be prescribed. A necessary and suffic...
We present a very short algebraic proof of a generalisation of the Farkas Lemma: we set it in a vector space of finite or infinite dimension over a linearly ordered (possibly skew) field; the non-positivity of a finite homogeneous system of linear inequalities implies the non-positivity of a...
Implications of the Farkas' Lemma; How to use the formula.KomornikVilmosLawsonJimmie D.American Mathematical MonthlyV. Komornick (1998), A simple proof of Farkas' lemma, American Math. Monthly, 105, 949-950.KOMORNIK, V.: A simple proof of Farkas' lemma, Am. Math. Monthly Decem- ber (...
Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using well-known arguments.Kager, Wouter...
An interesting analogue of Tucker's theorem for skew-symmetric matrices is derived for almost skew-symmetric matrices. Surprisingly, this analogue leads to a proof of Farkas' lemma.doi:10.1016/j.laa.2015.05.019Choudhury, Projesh NathSivakumar, K.C....
The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear...
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. Let V be a vector subspace of R n , and let intervals I 1 , , I n of real numbers be prescribed. A necessary and ...
Math. Mon. 87, 527–542 (1980; Zbl 0452.01007)], we do not use the convexity, separability, and duality properties; the idea of passage to the limit; the Bolzano-Weierstrass theorems, theorems of the alternative (Farkas lemma); implicit function theorems; Lyusterniks theorem; and'other ...