# A formalization of convex polyhedra based on the simplex method

arXiv: https://arxiv.org/abs/1706.10269 · HTML: https://mlsanity.com/paper/1706.10269/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [A Certified Proof Checker for Deep Neural Network Verification in Imandra](https://mlsanity.com/paper/2405.10611/) (2024)

## Abstract (arXiv)

We present a formalization of convex polyhedra in the proof assistant Coq. The cornerstone of our work is a complete implementation of the simplex method, together with the proof of its correctness and termination. This allows us to define the basic predicates over polyhedra in an effective way (i.e., as programs), and relate them with the corresponding usual logical counterparts. To this end, we make an extensive use of the Boolean reflection methodology. The benefit of this approach is that we can easily derive the proof of several fundamental results on polyhedra, such as Farkas' Lemma, the duality theorem of linear programming, and Minkowski's Theorem.