On Farkas' lemma and related propositions in BISH

On Farkas' lemma and related propositions in BISH

In this paper we analyse in the framework of constructive mathematics (BISH) the validity of Farkas' lemma and related propositions, namely the Fredholm alternative for solvability of systems of linear equations, optimality criteria in linear programming, Stiemke's lemma and the Superhedgi...

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Veröffentlicht in:Annals of pure and applied logic 2022-02, Vol.173 (2), p.103059, Article 103059
Hauptverfasser: Berger, Josef, Svindland, Gregor
Format: Artikel
Sprache:eng
Schlagworte:
Constructive game theory
Constructive mathematics
Farkas' lemma
Fredholm alternative
Stiemke's lemma
Superhedging Duality
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Zusammenfassung:In this paper we analyse in the framework of constructive mathematics (BISH) the validity of Farkas' lemma and related propositions, namely the Fredholm alternative for solvability of systems of linear equations, optimality criteria in linear programming, Stiemke's lemma and the Superhedging Duality from mathematical finance, and von Neumann's minimax theorem with application to constructive game theory.
ISSN:0168-0072
DOI:10.1016/j.apal.2021.103059