As of around 12:20, Central US Time, I also noticed this problem. I will keep closing out the notifications but they keep opening up. Will not be able to access PC for several days, hope it gets fixed by then. This is very, very disappointing and frustrating for an unexplained bug to happen on my computer, for no discernible reason whatsoever. Any fix, temporary or otherwise, would be greatly appreciated.
EDIT: Notifications have stopped, I believe the problem was due to the fact that my next "optimization" was scheduled for 7/30/2015, at 11:59 PM. Despite today being 7/31/15 at 12:50 AM. Maybe it's an issue with Avast's scheduling programming, maybe it's a complete coincidence. I also believe that perhaps it was due to the fact I had it scheduled for monthly cleanings, and it just so happened to land on exactly midnight? Not quite sure to be completely honest.