[Math] Can you give me good examples of non-convex functions that are problematic for optimization

Question

I want to test my extended gradient descent algorithm, whose aim is to handle non-convex problems better. Can you give me some examples of non-convex functions that are hard to minimize via gradient descent or heavy-ball methods? I will try to use these functions for testing purposes.

Answer 1

A less-known example is $f(x):=x^2+\exp(-1/(100(x-1))^2)-1$ on the closed interval $[-2,2]$. It takes $-.0067419337989203 $ at $x = .996387676055289 $.
See that discussion in MaplePrimes for more details.