Hey all. Let me get right to it!(adsbygoogle = window.adsbygoogle || []).push({});

I have the following objective function: [tex]\mathbf{minimize} \ \ trace((G^TG)^{-1})[/tex]

I am trying to minimize it with CVX.

I used schur complement to do the following:

[tex]

\begin{equation*}

\begin{aligned}

& \underset{G}{\text{minimize}}

& & \mathrm{trace}((G^TG)^{-1}) \\

\end{aligned}

\end{equation*}

[/tex]

which is equivalent to

[tex]

\begin{equation*}

\begin{aligned}

& \underset{t, G}{\text{minimize}}

& & \mathrm{t} \\

& \text{subject to}

&& t \geq\mathrm{trace}((G^TG)^{-1})

\end{aligned}

\end{equation*}

[/tex]

which is equivalent to

[tex]

\begin{equation*}

\begin{aligned}

& \underset{t, G, X, Z}{\text{minimize}}

& & \mathrm{t} \\

& \text{subject to}

&& t \geq\mathrm{trace}(Z) \\

&&&\begin{bmatrix} X & G^T \\G & I \end{bmatrix} \succeq 0 \qquad \\

&&&\begin{bmatrix} Z & I \\ I & X \end{bmatrix} \succeq 0 \qquad

\end{aligned}

\end{equation*}

[/tex]

Those two matrices introduced by schur complement achieve the following two inequalities: [tex]X \geq G^TG[/tex] and [tex]Z \geq X^{-1}[/tex]

My question is, is this formulation correct?

Here are some links that may be worth the read if you are interested:

The work I did is based on the following similar example.

I have had some help at the official cvx forums.

Thank you for reading : ) Any comments, pointers or advice is much appreciated!

EDIT: Apologies if this is in the wrong category.

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# Changing to SDP (optimization)

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