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Can anyone help we solve the following:

Find $X$ so that $F'(X)=0$

s.t.

$F(X)=hX^T-\frac{1}{2}X^T \Lambda_p X$

Where $X$ is a vector with elements $x_i$ and $Λ_p$ is a matrix with diagonal elements $λ_{ii}$ and off-diagonal elements $ρλ_{ij}$.

And the assumptions: $λ_{ii}$ is a constant $λ_0$ for all $i$, and $λ_{ij}=λ_{ji}$ for all $i$ and $j$. Further, $0≤λ_{ij}$ and for any $i$:

$$∑_jλ_{ij} =1-λ_0$$ Now find $X$ so that $F'(X)=0$.

I know the result is: $x_i=h/(λ_0+ρ(1-λ_0))$ for all $i$.

But I don't know how to get there. Can anyone help?

share|improve this question
    
You seem to have an undisplayable character - note that you can type mathematical symbols between dollars by using LaTeX, so between dollars \rho produces $\rho$, and so on. –  Matt Pressland Mar 7 '13 at 14:49
    
It occurs to me that maybe the character is displayable on your computer, so to help you identify it, it's the one between $\sum_j$ and $\lambda_{ij}$. –  Matt Pressland Mar 7 '13 at 15:13
    
Thanks, I hadnt noticed that. There should not be a character there at all. It sould simply read ∑_j λ_ij =1-λ_0 –  Ninja Mar 7 '13 at 20:12
    
OK - it's gone now. –  Matt Pressland Mar 8 '13 at 10:49

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