Cellular networks are optimized by targeting multiple objectives. Usually, the different objectives are not coherent: minimizing the transmit power; the number of base station (BS) sleep‐mode switchings, ie, active/sleep state transitions; and the activity of the BSs and guaranteeing the quality‐of‐service (QoS) of users. Hence, suitable trade‐offs have to be managed by network planners to provide an efficient solution to the challenge of booming mobile data. In this paper, we propose a multiobjective optimization framework aimed at minimizing the power consumption and the number of BS sleep‐mode switchings in cellular networks, by jointly considering QoS requirements. These requirements are expressed in terms of a required bit rate for each mobile terminal. The framework deals with network management, such as the number of BSs that should be switched on, considering common diurnal patterns of the traffic demand. The optimization technique proposed in this paper is mixed‐integer quadratic programming, which solves the joint power allocation and user association problem while also considering optimized bandwidth allocation schemes. The trade‐off between the conflicting objectives, as well as the performance analysis in terms of the throughput and energy consumption of the network, is shown for different traffic load cases. The proposed optimization can obtain up to 60% energy savings during off‐peak hours, guaranteeing QoS target requirements. By optimizing the network configuration, a 70% reduction in BS switch on/off operations can be reached in a day with 3% more energy expense.