While the problem of sum-rate maximization of the multiple-input multiple-output interference broadcast channel (MIMO IBC) has been extensively studied, most of the proposed solutions do not ensure a minimum rate for each scheduled user. In practice, many services require a minimum rate from the underlying communication links. Therefore, in this paper we consider a sum-rate maximization problem ... [Show full abstract] with per-link minimum rate constraints for the MIMO IBC. The key idea is scheduling a suitable subset of the communication links for simultaneous transmissions, such that a minimum rate for each scheduled link can be ensured. To this end, we pose the sum-rate maximization problem as a combinatorial optimization problem, in which we introduce binary variables to the classical transceiver design problem. We propose a centralized solution based on branch-and-bound and a hybrid semi-distributed scheme, in which a centralized unit is responsible for scheduling decisions, while the transceiver computations are distributed. Simulations show that the proposed solutions handle the user scheduling effectively, while the proposed hybrid scheme performs closely to the centralized scheme.