# Exploiting Sparsity in Complex Polynomial Optimization

arXiv: https://arxiv.org/abs/2103.12444 · HTML: https://mlsanity.com/paper/2103.12444/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

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

- [Sparse Polynomial Optimization: Theory and Practice](https://mlsanity.com/paper/2208.11158/) (2022)
- [GloptiNets: Scalable Non-Convex Optimization with Certificates](https://mlsanity.com/paper/2306.14932/) (2023)

## Abstract (arXiv)

In this paper, we study the sparsity-adapted complex moment-Hermitian sum of squares (moment-HSOS) hierarchy for complex polynomial optimization problems, where the sparsity includes correlative sparsity and term sparsity. We compare the strengths of the sparsity-adapted complex moment-HSOS hierarchy with the sparsity-adapted real moment-SOS hierarchy on either randomly generated complex polynomial optimization problems or the AC optimal power flow problem. The results of numerical experiments show that the sparsity-adapted complex moment-HSOS hierarchy provides a trade-off between the computational cost and the quality of obtained bounds for large-scale complex polynomial optimization problems.