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We consider a K link multiple-input multiple-output interference channel where each link consists of two full-duplex (FD) nodes. Two transmit beamforming design problems are solved: 1) sum-power minimization problem subject to rate constraints and 2) energy-efficiency maximization problem subject to individual power constraints. To tackle the sum-power minimization problem, we first generalize the well-known relationship between weighted-sum-rate (WSR) and weighted minimum-mean-squared-error (WMMSE) problems, originally used to solve the sum-rate maximization problems, and then propose a low complexity centralized algorithm, which converges to a stationary point. To decrease the exchange of a huge amount of data and excessive signaling traffic among the nodes, a distributed algorithm is also proposed. For the energy-efficiency maximization problem, the original fractional form optimization …