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We consider a network of cognitive users (also referred to as secondary users (SUs)) coexisting and sharing the spectrum with primary users (PUs) in an underlay cognitive radio network (CRN). Specifically, we consider a CRN wherein the number of SUs requesting channel access exceeds the number of available frequency bands and spatial modes. In such a setting, we propose a joint fast optimal resource allocation and beamforming algorithm to accommodate maximum possible number of SUs while satisfying quality of service (QoS) requirement for each admitted SU, transmit power limitation at the secondary network basestation (SNBS) and interference constraints imposed by the PUs. Recognizing that the original user maximization problem is a nondeterministic polynomial-time hard (NP), we use a mixed-integer programming framework to formulate the joint user maximization and beamforming problem. Subsequently, an optimal algorithm based on branch and bound (BnB) method has been proposed. In addition, we propose a suboptimal algorithm based on BnB method to reduce the complexity of the proposed algorithm. Specifically, the suboptimal algorithm has been developed based on the first feasible solution it achieves in the fast optimal BnB method. Simulation results have been provided to compare the performance of the optimal and suboptimal algorithms.