I believe for soft-reboot that plugging in the power cord will accomplish this. However, I do not believe there is any way to completely turn it off. I really wish there was, since I don't keep the proprietary cable with me and I wish that if I knew I wasn't going to use the watch for a day or two that I could power it off to save the battery. However, given there are no buttons besides the touch screen, I have no idea how you would signal the device to turn back on (save plugging in the cable) even if you did manage to power it off.
I'm using Garmin Express to update my Garmin Vivosport. Step 1 of 2 is to install the new software. Step 2 of 2 is to "restart your device". It wants me to eject and unplug my device from the computer which I can do. Then power it off and on and wait for the device to restart. I don't see how to do that, and this thread suggests it might not be possible. These are steps and instructions in Garmin Express specifically for the Vivosport! After restarting, I need to plug the device back in to the computer. Garmin express is stuck waiting for these steps to be done. I can't go back to the home or do anything with the Garmin Express. I can plug the Vivosport back into the computer, but the Garmin Express doesn't continue to complete the upgrade. If I try to quite Garmin Express I get an alarming warning saying if I quit while updating is in progress, my device3 may not work properly and/or may lose date. So, I'm completely stuck.