A second order cone characterization for sums of nonnegative circuits

The second-order cone (SOC) 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 SOCs, given that they have a strong expressive ability. In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits an SOC representation. Based on this, we give a new algorithm to compute SONC decompositions for certain classes of nonnegative polynomials via SOC programming. Numerical experiments demonstrate the efficiency of our algorithm for polynomials with a fairly large size (both size of degree and number of variables).