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We take two new approaches to design efficient algorithms for transmitter optimization under rate constraints in order to guarantee the Quality of Service for MIMO B-MAC interference networks. A B-MAC network is a generalized interference network that is a combination of multiple interfering broadcast channels (BC) and multiaccess channels (MAC). Two related optimization problems, maximizing the minimum of weighted rates under a sum-power constraint and minimizing the sum-power under rate constraints, are considered. The first approach takes advantage of existing algorithms for SINR problems by building a bridge between rate and SINR through the design of optimal mappings between them. The second approach exploits the polite water-filling structure, which is the network version of water-filling satisfied by all the Pareto optimal input of a large class of achievable regions of B-MAC networks. It replaces most generic optimization algorithms currently used for such networks and reduces the complexity while demonstrating superior performance even in non-convex cases. Both centralized and distributed algorithms are designed and the performance is analyzed in addition to numeric examples.