# Harmonic Hierarchies for Polynomial Optimization

arXiv: https://arxiv.org/abs/2202.12865 · HTML: https://mlsanity.com/paper/2202.12865/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2022.

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

- [Approximate Real Symmetric Tensor Rank](https://mlsanity.com/paper/2207.12529/) (2022)

## Abstract (arXiv)

We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in ℝn and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such hierarchies. We also introduce a novel optimization-free algorithm for building converging sequences of lower bounds for polynomial minimization problems on spheres. Finally some computational results are discussed, showcasing our implementation of these hierarchies in the programming language Julia.