I own a vintage jewelry store and I can tell you I have seen many items that were tarnished beyond what you would think was savable come back to life with a little elbow grease.
I don't know much about David Yurman in particular, but there are many modern jewelry companies that are now coating their metals in an anti-tarnish. You used to see this coating allot in the 60s and 70s on copper jewelry pieces like those by Renoir Matisse. This is why you don’t want to use a jewelry cleaner on the items, just a sofy polishing cloth. The cleaner damages the coating making it look worse than before. I also not a big fan of most of those jewelry cleaners that they sell in Dept. stores and places like Kays, Zale, etc. Allot of those cleaners are very toxic, and in my opinion too harsh. If you like the dip cleaners make sure it is a pearl safe cleaner like Jewel Brite. If it’s not pearl safe…don’t bother.
Now on to your necklace. The one over the counter thing you might try is Tarn-X. You can get it at most grocery store and places like Target. I use this in my shop on the heavily tarnished pieces with allot of luck. Read the instructions and make sure to wear gloves. Don’t use it if you pieces has any stones, enamel work, or artificially oxidized silver. If tarn-X won’t work for you, then try a silver paste polish. You’ll need allot of elbow grease for this method, but I have put a felt polishing wheel on my Dremel and used it with the paste with a light touch (caution, you can cause polish marks with this method if not careful).
If you want to send me a pic of the piece I might be able to get a better idea of what is going on and have some more suggestions. I'm kris at lilpaisley dot com