This paper addresses the optimization of a multicell network where each cell needs to select precoding matrices for beamforming in a distributed way. A modified version of the adaptive min-sum algorithm that considers reduced-size messages in the message-passing procedure is proposed. The message-passing technique, where each message is reduced to convey only part of usual information, is applied to maximize the system throughput leading to a faster adaptation procedure. Simulation results show this reduction leads to a small average performance loss in system throughput of approximately 6%, while generally reduces the message size in about 73%. Also, the proposed method still outperforms the baseline greedy technique.