Remotely Booting GS and HDX Endpoints After Shutdown

We have several cases a day where we have users hit the power button on our HDX remotes, and shut down our end points. This results in alerts, and a grumpy monitoring team on our end (not to mention, having to have someone run and fix it every time!)

I know that, if the codec is totally shutdown, I cannot bring it back via API calls....but is there another way to get them to power up remotely? Do they support wake on LAN? Is there a way to set them to automatically boot when they are plugged in (which would let me handl it with a switchable UPS?)

Basically, I am trying to figure out a way to bring them back up remotely, without having to go to the extent of installing an ethernet IR blaster in each room.