This work develops a novel power control framework for energy-efficient powercontrol in wireless networks. The proposed method is a new branch-and-boundprocedure based on problem-specific bounds for energy-efficiency maximizationthat allow for faster convergence. This enables to find the global solution forall of the most common energy-efficient power control problems with acomplexity that, although still exponential in the number of variables, is muchlower than other available global optimization frameworks. Moreover, thereduced complexity of the proposed framework allows its practicalimplementation through the use of deep neural networks. Specifically, thanks toits reduced complexity, the proposed method can be used to train an artificialneural network to predict the optimal resource allocation. This is in contrastwith other power control methods based on deep learning, which train the neuralnetwork based on suboptimal power allocations due to the large complexity thatgenerating large training sets of optimal power allocations would have withavailable global optimization methods. As a benchmark, we also develop a novelfirst-order optimal power allocation algorithm. Numerical results show that aneural network can be trained to predict the optimal power allocation policy.