  We present a novel efficient theoretical and numerical framework for solving
global non-convex polynomial optimization problems. We analytically demonstrate
that such problems can be efficiently reformulated using a non-linear objective
over a convex set; further, these reformulated problems possess no spurious
local minima (i.e., every local minimum is a global minimum). We introduce an
algorithm for solving these resulting problems using the augmented Lagrangian
and the method of Burer and Monteiro. We show through numerical experiments
that polynomial scaling in dimension and degree is achievable for computing the
optimal value and location of previously intractable global polynomial
optimization problems in high dimension.
