Hi everyone. I have this problem which I am trying to formulate. Basically, I have the following linear constraints:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

p_{11} = 2

[/tex]

[tex]

p_{22} = 5

[/tex]

[tex]

p_{33}+2p_{12}=-1

[/tex]

[tex]

2p_{13} =2

[/tex]

[tex]

2p_{23} = 0

[/tex]

And these are for the symmetric matrix

[tex]

\mathbf{P} =

\left( \begin{array}{ccc}

p_{11} & p_{12} & p_{13} \\

p_{12} & p_{22} & p_{23} \\

p_{13} & p_{23} & p_{33} \end{array} \right)

[/tex]

I would like to formulate a way to represent the linear constraints and [tex]\mathbf{P}[/tex] as a matrix at the same time.

I can do this using [tex]\mathbf{P}[/tex] or a vector of the entries of [tex]\mathbf{P}[/tex]. The linear constraints are easy if I use a vector ([tex]\mathbf{Ap}=\mathbf{b}[/tex], but then I don't know how to represent [tex]\mathbf{P}[/tex] as a matrix from the vector! And if I leave [tex]\mathbf{P}[/tex] as a matrix, all the constraints are easy to formulate except [tex]p_{33}+2p_{12}=-1[/tex]. Can anyone help me figure this out?

If anyone's curious, I'm trying to solve for [tex]\mathbf{P}[/tex] over the cone of PSD matrices using SDP. But I am entirely new to SDP and I'm scratching my head formulating this problem. I feel stupid right now :'(

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# Formulating Linear Constraints on a Matrix

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