  We propose a method for verifying that a given feasible point for a
polynomial optimization problem is globally optimal. The approach relies on the
Lasserre hierarchy and the result of Lasserre regarding the importance of the
convexity of the feasible set as opposed to that of the individual constraints.
By focusing solely on certifying global optimality and relaxing the Lasserre
hierarchy using necessary conditions for positive semidefiniteness based on
matrix determinants, the proposed method is implementable as a computationally
tractable linear program. We demonstrate this method via application to several
instances of polynomial optimization, including the optimal power flow problem
used to operate electric power systems.
