In this work, we address a joint energy efficiency (EE) and throughput optimization problem in interweave cognitive radio networks (CRNs) subject to scheduling, power, and stability constraints, which could be solved through traffic admission control, channel allocation, and power allocation. Specifically, the joint objective is to concurrently optimize the system EE and the throughput of secondary user (SU), while satisfying the minimum throughput requirement of primary user (PU), the throughput constraint of SU, and the scheduling and power control constraints that must be considered. To achieve these goals, our algorithm independently and simultaneously makes control decisions on admission and transmission to maximize a joint utility of EE and throughput under time-varying conditions of channel and traffic without a priori knowledge. Specially, the proposed scheduling algorithm has polynomial time efficiency, and the power control algorithms as well as the admission control algorithm involved are simply threshold-based and thus very computationally efficient. Finally, numerical analyses show that our proposals achieve both system stability and optimal utility.