Any mention of roundup/glysophosphate is a waste of time and money. Go get yourself some 24D (Agent White) and a good surfectant from Tractor supply. Prior to spraying it take a weed backer and chop the leaves up good. Spray with the 24D and surfectant mixture and it will take care of it in no time. You'll want to make sure that it can be on there for about 16 hours or so without getting wet/rained on. Check your weather.
Kudzu is easier than English Ivy. The above method is tried and true. Don't listen to anyone telling you to use diesel or ANYTHING with salt. Nothing will ever grow well if you salt the earth. That is why the Romans salted Carthage after sacking their city....so nothing could grow there again.
Have you ever tried hand cutting the vines with a utility knife right where they come out of the ground and then spraying the stumps with roundup weed killer?