  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 for unconstrained polynomial optimization via SOC
programming. We also provide a hybrid numeric-symbolic scheme which combines
the numerical procedure with a rounding-projection algorithm to obtain exact
nonnegativity certificates. Numerical experiments demonstrate the efficiency of
our algorithm for polynomials with fairly large degree and number of variables.
