For binary polynomial optimization problems (POPs) of degree d with n variables, we prove that the ⌈(n+ d− 1)/2⌉th semidefinite (SDP) relaxation in Lasserre’s hierarchy of the SDP relaxations provides the exact optimal value. If binary POPs involve only even-degree monomials, we show that it can be further reduced to ⌈(n + d − 2)/2⌉. This bound on the relaxation order coincides with the conject...
