  In contrast to Part I of this treatise [1] that focuses on the optimization
problems associated with single matrix variables, in this paper, we investigate
the application of the matrix-monotonic optimization framework in the
optimization problems associated with multiple matrix variables. It is revealed
that matrix-monotonic optimization still works even for multiple matrix-variate
based optimization problems, provided that certain conditions are satisfied.
Using this framework, the optimal structures of the matrix variables can be
derived and the associated multiple matrix-variate optimization problems can be
substantially simplified. In this paper, several specific examples are given,
which are essentially open problems. Firstly, we investigate multi-user
multiple-input multiple-output (MU- MIMO) uplink communications under various
power constraints. Using the proposed framework, the optimal structures of the
precoding matrices at each user under various power constraints can be derived.
Secondly, we considered the optimization of the signal compression matrices at
each sensor under various power constraints in distributed sensor networks.
Finally, we investigate the transceiver optimization for multi-hop
amplify-and-forward (AF) MIMO relaying networks with imperfect channel state
information (CSI) under various power constraints. At the end of this paper,
several simulation results are given to demonstrate the accuracy of the
proposed theoretical results.
