We consider the problem of joint admission control and power allocation in a multiband cognitive radio network (CRN) coexisting with multiple narrowband primary systems, and investigate two separate optimization problems: i) sum-rate maximization under primary user (PU) and secondary user (SU) quality of service (QoS) constraints; ii) sum-rate maximization and power minimization under PU and SU QoS constraints. We first show that these problems are NP-hard. Then we propose three different suboptimal algorithms for the first problem based on convex relaxation with tree pruning (CRTP), convex relaxation with gradual removal (CRGR) and genetic algorithms (GA). These algorithms offer different tradeoffs in terms of goodness of their solutions and computational complexity. For the second problem, we propose a multiobjective evolutionary algorithm which can generate a Pareto front in a time-efficient manner. Simulation results are provided to evaluate the proposed algorithms.