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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.

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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 $.
enter image description here See that discussion in MaplePrimes for more details.

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