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We consider the minimization of the average transmit power in a block-fading broadcast channel with time division multiple access under constraints on the average rates of all users. The globally optimal solution of this problem would require noncausal channel knowledge such that all blocks can be optimized jointly in advance, which is of course impossible in a practical system. However, it is possible to predict future channel realizations based on their statistical properties and on the observations of the current and past realizations. Therefore, we study a receding horizon optimization, where future fading blocks are incorporated into the optimization by means of an MMSE channel prediction or by means of a rate prediction method proposed in this paper. While the optimization based on channel prediction does not lead to the desired reduction of the average transmit power, the rate-prediction-based method is able to achieve a notable reduction.