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A wireless communication scenario is considered with K single-antenna source-destination pairs communicating through several half-duplex amplify-and-forward MIMO relays where each source is targeting only one destination. The relay beamforming matrices are designed in order to minimize the total power transmitted from the relays subject to quality of service constraints on the received signal to interference-plus-noise ratio at each destination node. Due to the nonconvexity of this problem, several approximations have been used in the literature to find a computationally efficient solution. A novel solution technique is developed in which the problem is decomposed into a group of second-order cone programs (SOCPs) parameterized by K phase angles; each associated with one of the constraints. An iterative algorithm is proposed to search for the phase angles and the relay beamforming matrices sequentially. However, convergence to the global optimal beamforming matrices cannot be guaranteed. Two methods for searching for the optimal values of the phase angles are proposed (from which the optimal beamforming matrices can be obtained) using grid search and bisection and the convergence of these methods to the global optimal solution of the problem is proved. Numerical simulations are presented showing the superior performance of the proposed algorithms compared to earlier suboptimal approximations at the expense of a moderate increase in the computational complexity.