# Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials

arXiv: https://arxiv.org/abs/2211.04889 · HTML: https://mlsanity.com/paper/2211.04889/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2022.

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

- [Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert](https://mlsanity.com/paper/2308.09474/) (2023)
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## Abstract (arXiv)

We consider the unconstrained optimization of multivariate trigonometric polynomials by the sum-of-squares hierarchy of lower bounds. We first show a convergence rate of O(1/s2) for the relaxation with degree s without any assumption on the trigonometric polynomial to minimize. Second, when the polynomial has a finite number of global minimizers with invertible Hessians at these minimizers, we show an exponential convergence rate with explicit constants. Our results also apply to minimizing regular multivariate polynomials on the hypercube.