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