ADAM does not work on simple convex problems [1].
[1] https://parameterfree.com/2020/12/06/neural-network-maybe-evolved-to-make-adam-the-best-optimizer/
[2] https://arxiv.org/pdf/1905.09997
[1] refers to [2], which shows that ADAM is not as efficient as gradient descent with line search on some problems, including neural networks.
I'll point out that "does not work" is not the same as "not as efficient" :) But it does seem the Adam paper had an error.
I think that Nesterov's first order method is the most efficient general first order algorithm on convex problems, so anything else is in some sense worse. (Edit: removed incorrect ADAM comment.)