SONC optimization and exact nonnegativity certificates via second-order cone programming

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 interesting both in theory practice to investigate which admit representation using SOCs, given that they have strong expressive ability. In this paper, we prove constructively the sums nonnegative circuits (SONC) admits SOC representation. Based on this, give new algorithm for unconstrained polynomial optimization via We also provide hybrid numeric-symbolic scheme combines numerical procedure rounding-projection obtain exact nonnegativity certificates. Numerical experiments demonstrate efficiency our polynomials fairly large degree number variables.