Non-orthogonal multiple access (NOMA) is a technology proposed for next generation cellular networks because of its high spectral efficiency and enhanced user connectivity. However, in the literature the optimal joint power and sub-carrier allocation for NOMA has been proposed for single cell only. Consequently, a global optimal algorithm for the joint power and sub-carrier allocation for NOMA system in multi-cell scenario is still an open problem. In this work, we propose a polyblock optimization based algorithm for obtaining a global optimal solution. It has reduced complexity due to a necessary and sufficient condition for feasible successive interference cancellation (SIC). Besides, we can adjust its optimization approximation parameter to serve as benchmark solution or to provide suitable solution for multi-cell multi-carrier NOMA systems. Numerical studies have shown its effectiveness.