Coordinated downlink multi-point transmission with joint processing is considered for weighted sum rate maximization with limited backhaul connectivity. The cooperating base stations are assumed to form a network with a tree topology. The limited backhaul capacity is modeled as the maximum number of active users per base station. The combinatorial user admission problem is solved via a novel approach based on the alternating method of multipliers (ADMM), which divides the joint transmit beamformer design and the user allocation into separate subproblems each with a tractable complexity. In addition to the ADMM design, we propose a low complexity l1 norm relaxation technique, which circumvents the combinatorial user allocation problem. The proposed schemes are shown to provide improved sum rate when compared to conventional coordinated beamforming and greedy user admission.