During operation, cellular network deployments undergo dynamic adaptations to balance coverage and capacity with energy efficiency and operating cost requirements. In this work, we propose a comprehensive objective function for cellular network optimization centered around the achievable end-user throughput, which is differentiable with respect to the received signal strength from individual transmitters. In contrast to pure SINR-based optimization, our formulation includes the cell assignment to account for limited resources shared by connected \UEs. Based on this objective, we study the joint transmit power optimization for a real-world network deployment under an energy efficiency constraint promoting sparse cell activations. Our results show that the lightweight GD scheme enabled by the differentiable formulation outperforms the black-box Bayesian Optimization baseline while offering reduced computational complexity and improved scalability. We can reliably trade off end-user throughput targets against energy consumption and switch off sectors during times of low demand, while ensuring adequate interference management and an even distribution of UEs among cells.