Weed killer for lawns, containing the active ingredient 2,4-D, will kill them but it will take multiple applications. If you buy the concentrate then add a few drops of dish soap to the diluted solution to help it stick. Violets have a waxy coating that makes them resistent to herbicides.
I have another chemical that I got from a lawn care supply company that works better and also works well on ground ivy but even that one takes two or three applications. I can't remember the name; I'll try to remember to go look at the bottle this evening.