# An Approach to Constrained Polynomial Optimization via Nonnegative Circuit Polynomials and Geometric Programming

arXiv: https://arxiv.org/abs/1602.06180 · HTML: https://mlsanity.com/paper/1602.06180/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant](https://mlsanity.com/paper/2209.06175/) (2022)

## Abstract (arXiv)

In this article we combine two developments in polynomial optimization. On the one hand, we consider nonnegativity certificates based on sums of nonnegative circuit polynomials, which were recently introduced by the second and the third author. On the other hand, we investigate geometric programming methods for constrained polynomial optimization problems, which were recently developed by Ghasemi and Marshall. We show that the combination of both results yields a new method to solve certain classes of constrained polynomial optimization problems. We test the new method experimentally and compare it to semidefinite programming in various examples.