# Polynomial Matrix Inequalities within Tame Geometry

arXiv: https://arxiv.org/abs/2206.03941 · HTML: https://mlsanity.com/paper/2206.03941/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [Taming Binarized Neural Networks and Mixed-Integer Programs](https://mlsanity.com/paper/2310.04469/) (2023)
- [Piecewise Polynomial Regression of Tame Functions via Integer Programming](https://mlsanity.com/paper/2311.13544/) (2023)

## Abstract (arXiv)

Polynomial matrix inequalities can be solved using hierarchies of convex relaxations, pioneered by Henrion and Lassere. In some cases, this might not be practical, and one may need to resort to methods with local convergence guarantees, whose development has been rather ad hoc, so far. In this paper, we explore several alternative approaches to the problem, with non-trivial guarantees available using results from tame geometry.