# An algorithm to compute the Hoffman constant of a system of linear constraints

arXiv: https://arxiv.org/abs/1804.08418 · HTML: https://mlsanity.com/paper/1804.08418/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2018.

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

- [A Computational Tropical Geometry Framework for Neural Networks](https://mlsanity.com/paper/2405.20174/) (2024)

## Abstract (arXiv)

We propose a combinatorial algorithm to compute the Hoffman constant of a system of linear equations and inequalities. The algorithm is based on a characterization of the Hoffman constant as the largest of a finite canonical collection of easy-to-compute Hoffman constants. Our algorithm and characterization extend to the more general context where some of the constraints are easy to satisfy as in the case of box constraints. We highlight some natural connections between our characterizations of the Hoffman constant and Renegar's distance to ill-posedness for systems of linear constraints.