I need to find a (global) minimum for a vector function.

\[Psi][x_] := N[1/2 F\[Phi][x].F\[Phi][x]]

where:

x is {x1,...,xn}

Fphi is another vector function that returns a vector (so Fphi(x).Fphi(x) is scalar).

If I use Minimize Mathematica returns

In[12]:= Minimize[{\[Psi], x > 0}, x]

Out[12]= {\[Psi], {x -> 1}}

What does it means? x->1....

x= {1,...,1} isn't a minimum for Psi.

How do I do it?