Press the power button on the monitor.
Or, build a robot hand to press the button and write a program to make it press the button.
Seriously, this isn't going to be easy. When a PC goes into power saving mode, it can switch off the signal from the video card which will put the monitor into power saving mode. The standard
Java API certainly does not have any functionality to control this. Maybe your operating system has functions to do this, which you could call via JNI from Java.