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We consider the problem of designing hybrid analog-digital beamformers in a downlink multi-user large-scale MIMO system. The objective is to minimize the total transmit power, while fulfilling SINR targets of all users. A dual virtual uplink problem is formulated for the original downlink problem based on the uplink-downlink duality theory, in order to decouple the digital beamformers in the constraints. Furthermore, an optimal method and a sub-optimal iterative method are devised to compute solutions of the hybrid beamforming problem. Simulation results demonstrate that the iterative method yields nearly optimal performance, despite its remarkably low complexity.