Is there a closed form solution to this constrained quadratic optimization problem?
$$ \mathrm{argmax}_X\ \mathrm{Tr}(AX)\mathrm{Tr}(BX)\\ 0\preceq X\preceq I $$
Where $A$ and $B$ are hermitian positive matrices and $A\preceq I$, $B\preceq I$.
EDIT: The inequalities are with respect to the eigenvalues