Update on my situation. I had been out of town since the day after Christmas so I didn't get to play around until I got back yesterday.
My set-up:
Late 2014 Mac Min 2.8 Ghz Standard config
Brand New Viewsonic VX2252MH
I had the monitor connected HDMI Port on Mini to HDMI Port on Monitor. When the computer allowed monitor to go to sleep, the only way to wake monitor back up was by power cycling monitor. If the computer was asleep, pressing spacebar on wireless keyboard would wake up computer (light turned from blinking to solid), then I would have to power cycle monitor to get it to wake up. With the setting set to allow the Mini to go to sleep if monitor was off, then I would sometimes have to turn off the Mini and back again to wake it up. I quickly disabled that part and just set computer to let hard drive sleep and to let monitor sleep. I was able to wake everything up like this, but cycling the monitor power button.
Before returning home I ordered an Amazon (Cables Matter brand) mini displayport to DVI cable. This is a single cable, not an adapter requiring a separate cable. So I now am using the mini displayport on computer and the DVI port on the monitor. So far, so good. I can, while logged on, tell the mini to sleep, which in turn makes the monitor go to sleep after a few seconds. With a press the spacebar everything comes back after a few seconds. I can allow the mini to put the monitor to sleep after a certain amount of time on its own and it will wake up everything with a spacebar push both when logged on to a profile and from the login screen.
For me this works. I had originally chosen the Viewsonic monitor to use the HDMI so I could use its internal speakers. It turns out the speakers on the monitor are useless, with the Mini's internal sound, believe it or not, being superior. Therefore, the loss of the sound signal by not being able to use HDMI is not a big loss. I also bought the cable, so the solution is no more clunky than an HDMI cable; unlike having an adapter of some sort plus a cable. I am fortunate that monitor had HDMI and DVI ports. If I was forced to downgrade to D-Sub 15 I would be livid.....
Regardless, this is unsatisfactory. I shouldn't have to find a solution to make a brand new computer work. And I do say computer, not monitor. Some people here have very modestly prefaced their statements with the fact they are not electrical engineers. Well, I am, and it is clear to me that this is soley an APPLE issue. It is also interesting that various Apple products over the years have had varying HDMI issues. This one, though, seems to be the worst, since it's not limited to rare configurations. Like I said, I was out of town and didn't have time to call Apple and place a formal request for support. I will do so, as soon as I get settled in.