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This paper studies the downlink beamforming design problem in multi-user multi-input-multi-output (MIMO) systems. Specifically, two related scenarios are considered: max-min signal-to-noise ratios (SNR) in wireless multicasting and max-min power in wireless power transfer (WPT). The conventional approach recasts the original nonconvex problems into convex semidefinite programming (SDP) by applying semidefinite relaxation (SDR) technique. This approach directly optimizes the transmit beamforming vector, thus suffers from high computational complexity when the number of transmit antennas at the base station (BS) is large. In this paper, we propose a unified and optimal beamforming structure which is expressed as a linear combination of the channel vectors of all users. With this proposed structure, the problem of beamforming design is thus simplified to optimize the combining weight vector, the …