You don’t want that invasive thug to get any more established. Yes it’s vinca, and you may have brought it in, but… It may have Found it’s own way in… Invasive means… That it invades. I’d dig it out and keep digging it out. Like Japanese honeysuckle, that stuff is really tenacious, and we have to stay after it, lest it kill everything native in its path.

I’m pretty sure that’s a blue periwinkle (Vinca minor). I’d let it become ground cover. It IS rather invasive, but will also grow where grass won’t. If you insist on killing it (or just need to keep it at bay somewhat) a glyphosate weed killer will help. http://homeguides.sfgate.com/stop-periwinkle-spreading-85868.html