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

4$\begingroup$ Standard test problems include en.wikipedia.org/wiki/Rosenbrock_function en.wikipedia.org/wiki/Rastrigin_function and for many more see geatbx.com/download/GEATbx_ObjFunExpl_v37.pdf $\endgroup$– Nawaf BouRabeeOct 30, 2016 at 16:45
1 Answer
A lessknown example is $f(x):=x^2+\exp(1/(100(x1))^2)1$ on the closed interval $[2,2]$. It takes $.0067419337989203 $ at $x = .996387676055289 $.
See that discussion in MaplePrimes for more details.