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

TL;DR

This paper introduces a novel method combining nonnegative circuit polynomials and geometric programming to solve certain constrained polynomial optimization problems, demonstrating competitive performance against semidefinite programming.

Contribution

The paper develops a new approach that integrates nonnegative circuit polynomial certificates with geometric programming techniques for constrained polynomial optimization.

Findings

The new method effectively solves specific classes of constrained polynomial problems.

Experimental results show competitive performance compared to semidefinite programming.

The approach broadens the toolkit for polynomial optimization with potential computational advantages.

Abstract

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.