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From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra ((Co)algebraic pearls)

Authors Filippo Bonchi , Alessandro Di Giorgio , Fabio Zanasi

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  • 19 pages

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Filippo Bonchi
  • University of Pisa, Italy
Alessandro Di Giorgio
  • University of Pisa, Italy
Fabio Zanasi
  • University College London, UK

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Filippo Bonchi, Alessandro Di Giorgio, and Fabio Zanasi. From Farkas' Lemma to Linear Programming: an Exercise in Diagrammatic Algebra ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 9:1-9:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Farkas' lemma is a celebrated result on the solutions of systems of linear inequalities, which finds application pervasively in mathematics and computer science. In this work we show how to formulate and prove Farkas' lemma in diagrammatic polyhedral algebra, a sound and complete graphical calculus for polyhedra. Furthermore, we show how linear programs can be modeled within the calculus and how some famous duality results can be proved.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
  • String diagrams
  • Farkas Lemma
  • Duality
  • Linear Programming


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