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Beamforming has the potential to improve the efficiency of simultaneous wireless information and power transfer (SWIPT) systems. Existing beamforming techniques have been focused on the downlink of SWIPT systems. In this paper, we optimize the beamformers and transmit duration to maximize the weighted sum rate of both the downlink and uplink in a multiuser multiple-input multiple-output (MIMO) SWIPT system. Specifically, we formulate and transform the problem into a weighted sum mean square error minimization, conduct difference of convex programming to decouple the downlink and uplink, and convert the problem to quadratic programming (QP), which can be solved iteratively in a centralized fashion. We also decentralize the QP problem using dual decompositions, and reduce the time-complexity without compromising the data rate. Moreover, our algorithms are extended to the case under imperfect channel state information. Confirmed by simulations, the proposed decentralization can dramatically reduce the time-complexity by orders of magnitude. The scalability of the proposed approach can be substantially enhanced to support medium to large networks.