  This work develops a novel power control framework for energy-efficient power
control in wireless networks. The proposed method is a new branch-and-bound
procedure based on problem-specific bounds for energy-efficiency maximization
that allow for faster convergence. This enables to find the global solution for
all of the most common energy-efficient power control problems with a
complexity that, although still exponential in the number of variables, is much
lower than other available global optimization frameworks. Moreover, the
reduced complexity of the proposed framework allows its practical
implementation through the use of deep neural networks. Specifically, thanks to
its reduced complexity, the proposed method can be used to train an artificial
neural network to predict the optimal resource allocation. This is in contrast
with other power control methods based on deep learning, which train the neural
network based on suboptimal power allocations due to the large complexity that
generating large training sets of optimal power allocations would have with
available global optimization methods. As a benchmark, we also develop a novel
first-order optimal power allocation algorithm. Numerical results show that a
neural network can be trained to predict the optimal power allocation policy.
