# How to minimize a vector function

Posted 9 years ago
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 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 returnsIn:= Minimize[{\[Psi], x > 0}, x]Out= {\[Psi], {x -> 1}}What does it means? x->1.... x= {1,...,1} isn't a minimum for Psi.How do I do it?
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Posted 9 years ago
 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 9 years ago
 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 9 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?