A short simple proof of closedness of convex cones and Farkas' lemma

Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using well-known arguments.

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Author: Kager, Wouter
Format: Article
Language:English
Online Access:Get full text
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Description
Summary:Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using well-known arguments.
ISSN:2331-8422
DOI:10.48550/arxiv.2208.11678