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....
A proof is given of Farkas's lemma based on a new theorem pertaining to orthogodal matrices. It is claimed that this theorem is slightly more general than Tucker's theorem, which concerns skew-symmetric matrices and which may itself be derived simply from tne new theorem. Farkas's lemma an...
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....
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 (...
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...
Although it is easy to prove the sufficient conditions for optimality of alinear program, the necessary conditions pose a pedagogical challenge. Awidespread practice in deriving the necessary conditions is to invoke Farkas'lemma, but proofs of Farkas' lemma typically involve "nonlinear" topics such ...
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.Projesh Nath ChoudhuryK.C. SivakumarLinear Algebra and Applications...
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...