We consider a bi-directional Full-Duplex (FD) Multiple-Input Multiple-Output (MIMO) communication system in which nodes are capable of performing transitter (TX)- Receiver (RX) digital precoding/combining and multi-tap analog cancellation, and have individual Signal-to-Interference-plus- noise Ratio (SINR) requirements. We present an iterative algorithm for the TX powers minimization that includes closed- form expressions for the TX/RX digital beamformers at each algorithmic iteration step. Our representative simulation results demonstrate that the proposed algorithm can reduce residual Self-Interference (SI) due to FD operation to below −110dB, which is the typical noise floor level for wireless communications. In addition, our design outperforms relevant recent solutions proposed for 2-user MIMO systems (the so called MIMO X channel) in terms of both power efficiency and computational complexity.