Yours' "not as efficient" in [2] means that, sometimes, ADAM "does not work." Look at figure 2, ADAM literally does not work in the case of "true model."

Yes, apologies, I didn't read the articles you linked before posting this. I did update the comment.

I don't think this changes the point, which is that most optimization methods used in AI owe a substantial intellectual debt to convex optimization theory.