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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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 Bou-RabeeCommented Oct 30, 2016 at 16:45
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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 $.
See that discussion in MaplePrimes for more details.
