Because the partial Lagrangian given by (18) remains the
same regardless of the value of Nr, the convergence proof of
Corollary 1 is almost the same as that for Theorem 1. Owing
to this convergence result together with the convergence of
SCA in Section IV-A, we can conclude that Algorithm 2, the
two-layer iterative algorithm, achieves at least a local optimum
of (38).