On Farkas' Lemma and Related Propositions in BISH
Josef Berger, Gregor Svindland
TL;DR
This paper examines the validity of key linear algebra and optimization propositions within constructive mathematics, providing insights into their applicability and limitations in a constructive framework.
Contribution
It offers a constructive analysis of Farkas' lemma and related propositions, extending their understanding in the context of BISH (Constructive Mathematics).
Findings
Farkas' lemma is analyzed constructively, revealing conditions for its validity.
Constructive versions of the Fredholm alternative and Stiemke's lemma are developed.
Applications to linear programming, finance, and game theory are discussed.
Abstract
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.
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