Exposed extreme rays of the SONC cone

TL;DR

This paper characterizes the exposed extreme rays of the SONC cone, providing a combinatorial criterion and explicit functionals to aid in optimization and analysis of nonnegative polynomials.

Contribution

It offers a complete, explicit combinatorial characterization of exposed extreme rays of the SONC cone, including constructive proofs and exposing functionals.

Findings

Complete characterization of exposed rays

Explicit combinatorial criterion

Constructive methods for detection

Abstract

We provide a complete and explicit characterization of the exposed extreme rays of the cone of sums of nonnegative circuit (SONC) polynomials. The criterion we derive is purely combinatorial and depends only on the existence of certain circuits within the ground set and on the nature of the corresponding extreme ray. Our constructive proofs also yield explicit exposing functionals, offering a basis for algorithmic detection of exposed rays in SONC-based optimization.