# A second order cone characterization for sums of nonnegative circuits

arXiv: https://arxiv.org/abs/1906.06179 · HTML: https://mlsanity.com/paper/1906.06179/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2019.

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

- [Sparse Polynomial Optimization: Theory and Practice](https://mlsanity.com/paper/2208.11158/) (2022)
- [Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant](https://mlsanity.com/paper/2209.06175/) (2022)

## Abstract (arXiv)

The second-order cone is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit a representation using second-order cones, given that they have a strong expressive ability. In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits a second-order cone representation. Based on this, we give a new algorithm to compute SONC decompositions for certain classes of nonnegative polynomials via second-order cone programming. Numerical experiments demonstrate the efficiency of our algorithm for polynomials with a fairly large size.