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For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables, e.g., precoders, equalizers, and training sequences, are usually matrices. It is well known that matrix operations are usually more complicated compared with their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper, we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then, exploiting the framework of matrix-monotonic optimization the optimal …