Deal with overflow in exp using numpy

You can use the bigfloat package. It supports arbitrary precision floating point operations.

http://packages.python.org/bigfloat/

import bigfloat
bigfloat.exp(5000,bigfloat.precision(100))
# -> BigFloat.exact('2.9676283840236670689662968052896e+2171', precision=100)

Are you using a function optimization framework? They usually implement value boundaries (using penalty terms). Try that. Are the relevant values really that extreme? In optimization it's not uncommon to minimize log(f). (approximate log likelihood etc etc). Are you sure you want to optimize on that exp value and not log(exp(f)) == f. ?

Have a look at my answer to this question: logit and inverse logit functions for extreme values

Btw, if all you do is minimize powellBadlyScaled(x,y) then the minimum is at x -> + inf and y -> + inf, so no need for numerics.

You can use numpy.seterr to control how numpy behaves in this circumstance: http://docs.scipy.org/doc/numpy/reference/generated/numpy.seterr.html

You can also use the warnings module to control how warnings are or are not presented: http://docs.python.org/library/warnings.html

Try scipy's -

scipy.special.expit(x).

Maybe you can improve your algorithm by checking for which areas you get warnings (it will probably bellow certain values for X[ 0 ],X[ 1 ]), and replacing the result with a really big number. You need to see how your function behaves, I thing you should check e.g. exp(-x)+exp(-y)+x*y