Farkas' Lemma and Motzkin's Transposition Theorem

Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐

January 17, 2019

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

We formalize a proof of Motzkin's transposition theorem and Farkas' lemma in Isabelle/HOL. Our proof is based on the formalization of the simplex algorithm which, given a set of linear constraints, either returns a satisfying assignment to the problem or detects unsatisfiability. By reusing facts about the simplex algorithm we show that a set of linear constraints is unsatisfiable if and only if there is a linear combination of the constraints which evaluates to a trivially unsatisfiable inequality.

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BSD License

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Session Farkas

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× 
@article{Farkas-AFP,
  author  = {Ralph Bottesch and Max W. Haslbeck and René Thiemann},
  title   = {Farkas' Lemma and Motzkin's Transposition Theorem},
  journal = {Archive of Formal Proofs},
  month   = {January},
  year    = {2019},
  note    = {\url{https://isa-afp.org/entries/Farkas.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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