I have a notebook with HDMI out and a mini DisplayPort Out. Both are connected to seperate monitors (dual monitor setup). I am running Ubuntu 18.10 on a NVidia 1070 QMax.
In normal operation the setup works. However, when I lock the screen or the system goes into power saving mode, the HDMI monitor works as expected and turns itself off. The mDP monitor, however, turns itself off just to turn itself on again after like 5 secs. This keeps on happening indefinately. After a minute or so it turns itself off again (probably sleep signal from Ubuntu) just to turn itself on again after a couple of seconds.
Besides that, I have the lid of my notebook open, too. The screen itself turns itself on and off in sync with my mDP monitor. All that happens while the HDMI one is still sleeping nicely.