i dont know anything about the varieties you're talking about. but for the regular orange sweet potatos at the american grocery stores you let the potato sprout in a dark place like in the pantry. once you get some sprouts that are about 4 inches long, carefully cut it off and set it in a small cup of water. in about 3-4 days it'll have roots about 1/2" long. from there i plant them in the raised beds.

once you get a few of them growing long outside, cut off the tips and stick them in the ground for more plants. after a month or two, mulch the plants. a few months later you should be able to dig out some tubers.

i have tried several times with the (hawaii/okinawa) purple sweet potatos without any luck. i love the purple ones.

I am not sure that I understand your question. All varieties of sweet potatoes have edible foliage. We have a large Korean population here, who seem to prefer the foliage to the potatoes. Part of it may be that just think we are silly because we never thought of eating the foliage. Does not seem to be any varietal preference altho certainly a vining variety would be preferred for production. Even an ornamental variety should be allright for foliage, altho the potatoes may be sparse and poor quality.
Sweet potatoes are tender perennials. Can't take any frost, which is why they are grown as annuals in temperate climates. They do have a long season and a deep root.
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I found this interesting as I am always looking for ways to use all parts of vegetables if possible. If you don't mind clarifying:

1. All variety of sweet potato(Ipomoea batatas)have edible leaves?
2. Is there a special variety of sweet potato that is grown specifically for the leaves?

Thanks again as I didn't know, and would have been especially worried that unlike the regular potato (Solanum tuberosum)which has poisonous leaves, these are safe to eat. Learn something new every day!

As far as I know, you should be able to just stick the sweet potato stems in the soil, keep well watered and they should grow tubers at some point.

I assure you Koreans also eat the tubers - sometimes raw!

I much prefer the asian varieties - korean and japanese for the tubers.

It's true that all sweet potato leaves are "edible"... which only means they won't kill you if you eat them. ;-) Whether they are palatable is another matter.

I've tried several varieties of sweet potato leaves as boiled greens, and there were considerable differences in taste. An orange-rooted variety (from the supermarket) had tough leaves. Two ornamental varieties I tried had very unpleasant flavor, almost chemical... about as appetizing as eating pine needles.

The shoots sold in Asian stores are the best varieties for leaves. There seem to be several different varieties grown for their leaves. The heavily-cut leaves of "kamote" that I grew in San Diego (from a Filipino store) were different from the more rounded leaves of the variety that I purchased from an Asian market where I live now. I don't know the variety name of either one, but both have white tubers.

As for the tubers: I've mentioned previously on this forum that the variety I grow now for leaves - while very good for that purpose - is unsuitable for tubers. When I first dug up the plants at the end of one season, I wondered why there were so few tubers under the plants. Then I noticed that there were several thick roots leading horizontally away from each plant, and dug carefully to follow one. I found a tuber over two feet away, and almost a foot deep!!! The tubers were dry & tasty, but the massive amount of excavation required to find them all made harvest of more than a few impractical.

This question has come up quite a few times on this forum, without a definitive answer... but there is a possible solution. You might want to contact Glen Drowns of Sandhill Preservation Center. He is a collector of sweet potato varieties, and offers a huge number of them, both heirloom & commercial. He might be able to steer you to one that suits your needs.

If you find some that you like at the Asian store, they should be very easy to start from rooting a few cuttings.

I noticed that Duck Creek Farms sells a sweet potato variety listed as "Asian Greens Variety", with a catalog description of

"We received this variety from an Asian grower that grew them for greens, we do not know the type of roots it makes yet or the real name, but the vines were very good cooked liked spinach."

Here is a link that might be useful: Duck Creek Farms - sweet potatoes

I have lived in S.C. all my life & we eat corn, peas & sweet potatoes raw.
Koreans are not the only Asians to eat sweet potato leave.
I first heard about wilting the leaves in a frying pan & salt & pepper to taste, at a Chinese restaurant.