  In this work we present some exactness conditions for the Shor relaxation of
diagonal QCQPs, which extend the conditions introduced in different recent
papers about the same topic. It is shown that the Shor relaxation is equivalent
to two convex quadratic relaxations. Then, sufficient conditions for the
exactness of the relaxations are derived from their KKT systems. It will be
shown that, in some cases, by this derivation previous conditions in the
literature, which can be viewed as dual conditions, since they only involve the
Lagrange multipliers appearing in the KKT systems, can be extended to
primal-dual conditions, which also involve the primal variables appearing in
the KKT systems.
