arXiv:2409.08119 Abstract | arXiv Analytics

arXiv:2409.08119 [math.OC]Abstract References Reviews Resources

Duality theory in linear optimization and its extensions -- formally verified

Published 2024-09-12Version 1

Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take ``infinite values''.

Comments: Code: https://github.com/madvorak/duality/tree/v2.0.0

Categories: math.OC, cs.LO

Keywords: linear optimization, extensions, extend duality theory, linear combination, infinite values

Tags: github project

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