Abstract

We formalize the weak and strong duality theorems of linear programming. For the strong duality theorem we provide three sufficient preconditions: both the primal problem and the dual problem are satisfiable, the primal problem is satisfiable and bounded, or the dual problem is satisfiable and bounded. The proofs are based on an existing formalization of Farkas’ Lemma.

BibTeX

@article{LP_Duality-AFP,
  author  = {René Thiemann},
  title   = {Duality of Linear Programming},
  journal = {Archive of Formal Proofs},
  month   = {February},
  year    = {2022},
  note    = {\url{https://isa-afp.org/entries/LP_Duality.html},
            Formal proof development},
  ISSN    = {2150-914x},
}