A short note on strong duality : without simplex and withouttheorems of alternatives - Lahiri, Somdeb (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2017)
We provide an alternative proof of the strong duality theorem whose main basis isthe proposition which says that every canonical linear programming minimization problemwhose image under its objective function of the set of feasible solutions is non-empty andbounded below has an optimal solution. Unlike earlier proofs, this proof uses neither thesimplex method nor Farkas’s lemma. We also use this proposition to obtain an independentproof of Farkas’s lemma.
Mathematical Economics; 2017; Nr 13 (20); s. 59-66
Keywords: LP problem; strong duality; Farkas’s lemma