Weber Performe SS (Black Frame) Restoration

[WeberGuy2020]

Hi Club Members, I am in the process of restoring my 2018 Performer SS.  I am not sure which cleanser I should use to refresh the slightly oxidized black frame.  I used some mild liquid soap but it didn't do the job.   I don't want to use anything too harsh as it may further penetrate the original finish.   Also, I noticed that there are some minor rust developed on some parts of the black frame.  Any good way to have this remedied?  Any suggestion will be greatly appreciated.