An upper bound for nonnegative rank

TL;DR

This paper establishes an upper bound on the nonnegative rank of rank-three matrices, enabling a minimal set of linear inequalities to describe convex polygons.

Contribution

It introduces a new upper bound for nonnegative rank in rank-three matrices, impacting convex polygon descriptions.

Findings

Upper bound for nonnegative rank of rank-three matrices

Minimal linear inequalities for convex n-gons

Enhanced understanding of matrix factorization constraints

Abstract

We provide a nontrivial upper bound for the nonnegative rank of rank-three matrices, which allows us to prove that [6(n+1)/7] linear inequalities suffice to describe a convex n-gon up to a linear projection.