Nonnegative Polynomials and Circuit Polynomials

The concept of sums nonnegative circuit (SONC) polynomials was recently introduced as a new certificate nonnegativity especially for sparse polynomials. In this paper, we explore the relationship between and SONCs. As first result, provide sufficient conditions with general Newton polytopes to be SONC, which generalizes previous result on simplex polytopes. Second, prove that every SONC admits decomposition without cancellation. other words, decompositions preserve sparsity polynomials, is dramatically different from classical sum squares key property design efficient algorithms polynomial optimization based decompositions.