NMinimize holding problem

Question

I have a function that I want to minimize numerically through an NMinimize command (because it's very complicated analytically). The minimizer call looks as follows:

NMinimize[{mat = func0[a, b, c, d, e, f]; Print[mat]; 
{ac0t, ac1t, ac2t, ac3t} = mat.{Ac0, Ac1, Ac2, Ac3}; 
{as0t, as1t, as2t, as3t} = mat.{As0, As1, As2, As3}; 
Total[({
  a+b,
  a^2+b^2,
  ...
  })^2], constraints}, {a, b, c, d, e, f},  Method -> "NelderMead"]

So notice that I'm minimizing a sum of squares, but before calculating the sum of squares, I have to calculate stuff using a function func0. func0 is defined as a numerical function:

func0[a_?NumericQ,b_?NumericQ,c_?NumericQ,d_?NumericQ,e_?NumericQ,f_?NumericQ]:=Module[{},...]

However, when it gets evaluated in the minimizer, it gets evaluated and held. So Print[mat] will result in func0[a, b, c, d, e, f], and not in a numerical value. While if I calculate this function outside NMinimze, it works fine. I can imagine that NMinimize is calling it with variables, and that's why it isn't working.

How can I tell NMinimize to take this only numerically?

Please advise. Thank you.

---

EDIT: As requested in comments, I'm adding an executable example of the problem:

func0[a_?NumericQ] := {{Sin[a Degree], Cos[a Degree]},{Sin[a Degree], Cos[a Degree]}}
NMinimize[{var = func0[a]; 
Print[var]; {aa, bb} = var.{1/Sqrt[2], 1/Sqrt[2]}; 
Total[{aa - bb, aa + bb
 }^2], a > 0}, {a}, Method -> "NelderMead"] 

If you execute this code, you'll see that an error will be thrown:

Set::shape: Lists {aa,bb} and func0[a].{1/Sqrt[2],1/Sqrt[2]} are not the same shape. >>

Which happens because func0[a] is being evaluated symbolically, while I must evaluate it numerically. Please note this is a simple example for the sake of argument. My func0 is very complicated and cannot be evaluated symbolically.

Answer 1

Its not func0[a] that is the problem; it's the compound expression you've given NMinimize to chew (look up the true meaning of ;). This compound expression is not a _?NumericQ function of a, so Mathematica can't tell that it is only valid for numeric values of a.

Try:

func1[a_?NumericQ] := (var = func0[a];   
   Print[var]; {aa, bb} = var.{1/Sqrt[2], 1/Sqrt[2]};
   Total[{aa - bb, aa + bb}^2]);

and...

NMinimize[{func1[a], a > 0}, {a}, Method -> "NelderMead"]