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How to minimize a vector function

Posted 10 years ago
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?
POSTED BY: Juri Bruciati
3 Replies
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]
POSTED BY: Frank Kampas
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.
POSTED BY: Frank Kampas
Posted 10 years ago
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?
POSTED BY: Juri Bruciati
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