# Exploiting constant trace property in large-scale polynomial optimization

arXiv: https://arxiv.org/abs/2012.08873 · HTML: https://mlsanity.com/paper/2012.08873/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2020.

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

- [Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant](https://mlsanity.com/paper/2209.06175/) (2022)
- [GloptiNets: Scalable Non-Convex Optimization with Certificates](https://mlsanity.com/paper/2306.14932/) (2023)

## Abstract (arXiv)

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result such moment relaxations can be solved efficiently by first-order methods that exploit CTP, e.g., the conditional gradient-based augmented Lagrangian method. We also extend this CTP-exploiting framework to large-scale POPs with different sparsity structures. The efficiency and scalability of our framework are illustrated on second-order moment relaxations for various randomly generated quadratically constrained quadratic programs.