# TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization

arXiv: https://arxiv.org/abs/2103.00915 · HTML: https://mlsanity.com/paper/2103.00915/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

## Built on by (most cited first, 3 of 3)

- [Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization](https://mlsanity.com/paper/2405.17049/) (2024)
- [Mixtures Closest to a Given Measure: A Semidefinite Programming Approach](https://mlsanity.com/paper/2509.22879/) (2025)
- [Recovering Lower-Dimensional Semialgebraic Support of a Measure from its Moments](https://mlsanity.com/paper/2609.33420/) (2026)

## Abstract (arXiv)

The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting correlative and term sparsity to obtain a new moment-SOS hierarchy involving potentially much smaller positive semidefinite matrices. TSSOS can be applied to numerous problems ranging from power networks to eigenvalue and trace optimization of noncommutative polynomials, involving up to tens of thousands of variables and constraints.