for teaching purposes, I am looking for continuous compact functions defined over one or two variables that are deliberately chosen to illustrate how optimization algorithms can run into difficulties, i.e., requiring unusually many iterations to solve.
I want to use this to show how different algorithms have strengths and weaknesses for certain functions.
most books have nice graphics showing why the steepest descent algorithm runs into problems. I want something like this for contrast with other algorithms, too, like Conjugate Priors (of various kinds), Newton-Raphson; and even global optimizers, like annealing, etc.
it is a big plus if the function is easy to write down parametrically, like
f(x)= -1/(abs(x))
I hope there is a paper somewhere that does this. pointers appreciated.