The NP-hard criterion for canonical dual optimization

Let $({\cal P})$ be the primal nonconvex optimization problem and let $({\cal P}^d)$ be its canonical dual problem. The canonical dual problem is called solvable when it has a solution in ${\cal S}^+_a$. NP-hard criterion. The problem $({\cal P})$ is NP-hard if its canonical dual $({\cal P}^d)$ is not solvable. This conjecture is proposed as a criterion distinguishing tractable instances solved through the canonical dual problem from cases requiring minimization over stationary points of a nonconvex feasible space. Its resolution is not given in the source.