Power up after UPS initiated shutdown I have a Mac Pro with an APC UPS supply connected.  I have it configured to shut down the system when we lose power.  What I'd like to do is to have it power up the system when power is subsequently restored, but I don't see any option that appears to do that.  I am using OS 10.12.4 and an APC Back-UPS Pro 1500VA.
Simply put, no. The APC/Apple software is designed for shutdown only. I'd been looking for a similar solution for years when I managed a few XServes, but my institution opted to provide massive battery backups and a gas-powered emergency generator when we moved to a double rack of Windows servers a few years ago.

This device 3Gstore Remote Power IP Switch - 1 Outlet looks like it might work. I am going to get one of my very own for a security web-cam I just installed at home.

Disclaimer: Not professionally or materially connected with 3Gstore.