How to minimize a vector function

Questions
1

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?

2

You didn’t give the argument x to the function psi in your Minimize call.
Also, note that you’re actually calling NMinimize because your function returns numerical values.

3

I know that what I wrote is wrong, but I can’t find out how to find a x={x1,…xn} that minimize Psi.
Is there a way to find a minimum if the function use vector?

4

Mathematica can’t tell how many components there are in x. I think you need to break x up into a List. Also, your constraint should be Thread[ x < 1]