Pythonic way to iterate through multidimensional space?

[Frank Miles]

I need to evaluate a complicated function over a multidimensional space
as part of an optimization problem.  This is a somewhat general problem
in which the number of dimensions and the function being evaluated can
vary from problem to problem.

I've got a working version (with loads of conditionals, and it only works
to #dimensions <= 10), but I'd like something simpler and clearer and
less hard-coded.

I've web-searched for some plausible method, but haven't found anything
"nice".  Any recommendations where I should look, or what technique should
be used?

TIA!