A few people contacted me with the question how the NDCG optimization in our NIPS07 paper on collaborative ranking is done in detail. Unfortunately, we did not manage to squeeze these details into the paper itself. Luckily, there is the internet and I just uploaded my notes on this to the CofiRank site. Please note that these notes are not peer reviewed. If you find a bug/typo/whatever in the derivations, I would be more than happy to hear from you!