Find the upper and lower boundaries of a multivariable function

Hello,

I am trying to find the boundaries of a somewhat complex function containing more than 3 variables at one time. The boundaries of each variable are known but the problem is that the function is considered not to be linear with regard to the variables (highest value for each variable does not necessarily mean highest value of the function). So we need to test some values between the boundaries.

The maximum number of variables in an equation at one time is 11.

Is there any way to do this other than the obvious one witch has an exponential complexity (for loop in a for loop in a for loop, etc...)