Does anybody know what this is?

[Junebug]

I've included a photo of what I would refer to as a weed or ground cover. It's viney with yellow flowers and shallow roots. It's very invasive and is taking over the better part of my yard on the west side of the house and is now popping up in the back yard. I've tried Scotts Weed & Feed and it didn't phase it a bit. It's not an ugly weed and stays green throughout the winter. I've tried pulling and pulling and digging and pulling. If a little piece gets broken it begins to grow again. I've thought of using a vegetation killer, but that would kill any grass that's remaining too. Does anyone know what this is?