  In this paper we examine a symmetric tensor decomposition problem, the
Gramian decomposition, posed as a rank minimization problem. We study the
relaxation of the problem and consider cases when the relaxed solution is a
solution to the original problem. In some instances of tensor rank and order,
we prove generically that the solution to the relaxation will be optimal in the
original. In other cases, we present interesting examples and approaches that
demonstrate the intricacy of this problem.
