Question: NLSolve Optimization minimize multiple variables to generate maximum in range

I have a function which describes the complex reflection coefficient of a structure with respect to frequency.  One or more variables may control the function, and I want to find the set of variables which yield the lowest maxima in frequency response, over a given range of frequencies.

For a simple example relying only on a single variable "Z", it would be something like this:

NLPSolve(

NLPSolve(abs(Gamma),f=f1..f2,maximize),

Z=Z[1]..Z[N],

initialpoint = [Z=Z[2]]

);

I suspect I am having two problems with the above:

1.  Without some numeric starting point for Z, the nested NLPSolve(Gamma,f=f1..f2,maximize), Gamma is failing to resolve to a maxima in the range f = f1..f2.  Testing NLPSolve(subs(Z=1,abs(Gamma)),f=0..1,maximize); works just fine, but not without fixing Z to some undesired point.

2.  Maple seems to be unhappy about the inclusion of abs(), stating "abs is not differentiable at non-real arguments".  However, a test of another simpler complex function did not bring about the same complaint, so perhaps this is a misleading error due to the poor structure of my command.

Help!

Thank you.