Is My SDP Formulation to Minimize trace((G^TG)^-1) Correct?

[perplexabot]

Hey all. Let me get right to it!

I have the following objective function: $$\mathbf{minimize} \ \ trace((G^TG)^{-1})$$
I am trying to minimize it with CVX.

I used schur complement to do the following:
$$\begin{equation*}<br /> \begin{aligned}<br /> & \underset{G}{\text{minimize}}<br /> & & \mathrm{trace}((G^TG)^{-1}) \\<br /> \end{aligned}<br /> \end{equation*}$$
which is equivalent to
$$\begin{equation*}<br /> \begin{aligned}<br /> & \underset{t, G}{\text{minimize}}<br /> & & \mathrm{t} \\<br /> & \text{subject to}<br /> && t \geq\mathrm{trace}((G^TG)^{-1})<br /> \end{aligned}<br /> \end{equation*}$$
which is equivalent to
$$\begin{equation*}<br /> \begin{aligned}<br /> & \underset{t, G, X, Z}{\text{minimize}}<br /> & & \mathrm{t} \\<br /> & \text{subject to}<br /> && t \geq\mathrm{trace}(Z) \\<br /> &&&\begin{bmatrix} X & G^T \\G & I \end{bmatrix} \succeq 0 \qquad \\<br /> &&&\begin{bmatrix} Z & I \\ I & X \end{bmatrix} \succeq 0 \qquad<br /> \end{aligned}<br /> \end{equation*}$$

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

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.

 

[perplexabot]

Answer here: http://math.stackexchange.com/questions/1555273/minimize-mathrmtrgtg-1
More discussion here: http://ask.cvxr.com/t/minimizing-trace-inverse-of-grammian/3135/35

Thank you for reading : )