Optimize with handling an objective function as "Black Box"

Is there a way to optimize a costrained objective function without really knowing its expression? For example, say we have :

 % main.m %
  % starting point and costraints all previously defined
 [Xopt,Fval] = fmincon(@obj,x0,A,B,Aeq,Beq,lb,ub,[],options);
 % End of main.m %

% Objective Function obj.m %
function [F] = obj(X)
   % Write Data into File for exe
   fopen('X.dat','w');                                    
   dlmwrite('X.dat',X); 
   fclose('all');

   % Run Black Box exe
   system('BB.exe') % where the expression of the objective function is(unknown to us)

   % Read Results from exe
   F = importdata('Fval.dat')
  % End of obj.m %

The above example does not work,but gives the general idea The code is also attached (Run main.m) with a very simple objective function.

Answer 1

[Sean de Wolski]

The pattern you have there looks like it should work and the idea is fine.

Though I would probably recommend patternsearch over fmincon since you likely cannot guarantee that BB.exe returns smooth continuous values.

Also note that F has to be a scalar. So maybe at the end:

F = norm(F)

[Ilias Seferlis]

that works perfectly! thanks a lot!

[Ilias Seferlis]

Is there any way to make it work with "fmincon"? I can't make it to work as explained above.