farkas’s lemma

Strong Duality: Without Simplex and without theorems of alternatives

  • Somdeb Lahiri
    • Categories Linear Programming Tags , ,

    The simplex method has its own problems related to degenerate basic feasible solutions. While such solutions are infrequent, from a theoretical standpoint a proof of the strong duality theorem that uses the simplex method is not complete until it has taken a few extra steps. Further, for economists the duality theorem is extremely important whereas … Read more

    A short derivation of the Kuhn-Tucker conditions

  • Yoshihiro Tanaka
    • Categories Constrained Nonlinear Optimization Tags , , ,

    The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions by applying a corollary of Farkas’s lemma under the Mangasarian-Fromovitz constraint qualification. Citation Discussion Paper Series A, No. 2011-234, Graduate School of Economics and … Read more