In cellular radio systems, transmitter power controls aim at achieving acceptable carrier-to-interference (C/I) ratios in all active communication links. All of the existing power control schemes focus on single channel control, which could not guarantee optimal performance if applied to the whole system containing multiple channels. This paper presents a full optimization model for the transmitter power control problem which deals with all channels and cells in the system simultaneously. With the limitations of computational speed and data updating ability, our model, at this moment, may not be appropriate for real-time power control. Rather, our model provides a performance standard that various practical real-time power control methods can achieve. This is important information in the design of a practical real-time system. To solve the optimization model, we use the Lagrangian relaxation technique. Our computational result shows that it is possible to reduce the overall blocking probability by 20 - 50% over the existing power control schemes.