Help on how to write a function to be used with NMinimize

Question

I need some help to write a proper function to be used as a parameter on NMinimize. Here is the code of the function to be minimized (Please correct, optimize and rewrite the code if you want to - I need to understand how to write proper Mathematica code).

plot[τ_, Ω_] := Module[{arg, abs, aux}, 
   {arg, abs} = 
     Factor[Together[ComplexExpand[Through[{Arg, Abs}[(1 + I*2*Ω)/(1 + I*2*τ*Ω)]]]]]; 
   aux = arg/Degree;
   aux = If[aux < 0, aux = 360 - aux, aux];
   {aux, 20*Log10[abs]}]

modFunction1[kc_, gp_, ω_, pm_, variable_:s] := Module[{arg, abs, aux}, 
  {arg, abs} = 
    Factor[Together[ComplexExpand[Through[{Arg, Abs}[kc*gp /. variable -> I*ω]]]]]; 
  aux = (-arg)*(180/Pi) + pm - 180;
  aux = If[aux < 0, 360 + aux, aux];
  {-20*Log10[abs], aux}]; 

functionF1[kc_, gp_, ω_, pm_, variable_:s, τ_, Ω_] := Module[{a, b, c, d}, 
  {a, b} = N[modFunction1[kc, gp, ω, pm, variable]];
  {d, c} = N[plot[τ, Ω]];
  (a - c)^2 + (b - d)^2]; 

and finally

NMinimize[functionF1[50, 100/(s*(s + 5)*(s + 10)), 9, 42, τ, Ω],
  {{τ, 10.5, 10.6}, {Ω, -0.1988, -0.1987}}]

NMinimize returns

NMinimize::nnum: "The function value 0.000459846 +(54.9326 -aux$584644)^2 is not a number at {[Tau],[CapitalOmega]} = {10.5919,-0.198714}"

but evaluating functionF1 on those same values returns a real number.

What am I missing? Any comment on how to write the code is most welcome. I definitely need some guide on how to write proper functions.

Answer 1

I'm putting the comments into an answer, the gist of it is very simple: The arguments in the function you need to minimize should be numeric. The trick with NumericQ that is suggested is covered here and here.