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

Abstract

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".

Code: https://github.com/madvorak/duality/tree/v3.2.0