I recommend using a Brillo Pad; these are very fine wire wool, impregnated with soap. These are cheap and very effective. Used these for about 4 years and tips stayed just like new. Its ideal for our stainless tips giving a polished result and not too aggressive. Dip the pad in hot water and rub away, just rinse off afterwards and all the black soot will have gone.

Autosol is good too, but takes much longer because you are relying on the abrasiveness of the cream while applying it on a cloth, so hard work getting inside the tips, and expensive.