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 problem is first transformed into an equivalent subtractive-form optimization problem by exploiting the properties of fractional programming, and then performs a dual-layer optimization scheme. In the outer layer, the energy-efficiency parameter is searched using a simple 1-D search, and in the inner layer, the relationship between WSR and WMMSE is exploited to solve the subtractive form optimization problem. Since the proposed algorithms require perfect channel-state-information, which is difficult to acquire in practice, we also propose a robust design, by taking the imperfect channel knowledge into consideration. It is shown in the simulations that the sum-power achieved in FD mode depends heavily on the transmitter/receiver distortion. Also the energy-efficiency of FD systems is lower than that of half-duplex systems, as FD nodes need to overcome self-interference and increased inter-user interference, which leads to high power consumption.