@vv 

Firstly, do you mean here by V^+ the transpose of V ?

the objective function to be mininized have this form:

f := (V.A.transpose(A).transpose(V))/(V.B.transpose(B).transpose(V))

Such as: A and B are known matrix and not a random matrix (A is a 22-by-22 matrix and B is a 22-by-11 matrix).

When i try to apply your code for my exemple, we have several problems :

1) V wasn't a random vector (V to be optimized is a 20-by-22 matrix that must satisfy an equality constraint : V.Ho=0 with Ho is a 22-by-2 matrix).

2) B wasn't a square matrix (B is a 22-by-11 matrix , we can't find the eigenvalues of a non square matrix).

3) Note that  n=22 >6 !!