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In a conventional wireless cellular system, signal processing is performed on a per-cell basis; out-of-cell interference is treated as background noise. This paper considers the benefit of coordinating base-stations across multiple cells in a multi-antenna beamforming system, where multiple base-stations may jointly optimize their respective beamformers to improve the overall system performance. Consider a multicell downlink scenario where base-stations are equipped with multiple transmit antennas employing either linear beamforming or nonlinear dirty-paper coding, and where remote users are equipped with a single antenna each, but where multiple remote users may be active simultaneously in each cell. This paper focuses on the design criteria of minimizing either the total weighted transmitted power or the maximum per-antenna power across the base-stations subject to signal-to-interference-and-noise-ratio (SINR) constraints at the remote users. The main contribution of the paper is an efficient algorithm for finding the joint globally optimal beamformers across all base-stations. The proposed algorithm is based on a generalization of uplink-downlink duality to the multicell setting using the Lagrangian duality theory. An important feature is that it naturally leads to a distributed implementation in time-division duplex (TDD) systems. Simulation results suggest that coordinating the beamforming vectors alone already provide appreciable performance improvements as compared to the conventional per-cell optimized network.