Abstract Iteratively decentralized weighted sum rate maximization (WSRMax) is proposed for multiple-input multiple-output (MIMO) interfering broadcast channel. Particular emphasis is given for improved rate of convergence for the WSRMax utility. Successive convex approximation is applied to provide an algorithm with fast rate of convergence and low computational complexity per iteration while sustaining the monotonic improvement of the objective. This method has particularly convenient structure for decentralized processing allowing alternating receive and transmit beamformer updates. This structure complies with recently proposed low overhead pilot aided beamformer signaling frameworks. The computational complexity and signaling overhead of the scheme are equivalent with the well-established weighted mean squared error minimization (WMMSE) approach. The proposed method is shown, by numerical examples, to improve the rate of convergence with respect to the WMMSE and semidefinite program (SDP) relaxation methods.