$$\begin{array}{ll} \underset{{\bf A} \in \Bbb R^{n \times h}}{\text{maximize}} & \log \det \left({\bf I} + {\bf Z} {\bf Z}^{T}\right)\\ \text{subject to} & {\bf Z} = {\bf A} {\bf X} \\ & \| {\bf Z} \|_{\text{F}} = 1 \end{array}$$
where ${\bf X} \in \Bbb R^{h \times m}$ and ${\bf Z} \in \Bbb R^{n\times m}$. There is no restriction on whether $n$ or $m$ is larger. Also, $h>n$.
How can I efficiently analyze and solve this optimization problem? Are there good reformulations or relaxations to it, or any efficient/special algorithms I shall investigate?