Can anyone see a way to solve this equation efficiently?
$$AXB + X\odot C = D$$
I tried a straightforward solution that involved vectorizing $X$ but that turned out too expensive for my application -- my matrices are all $d\times d$ with $d=1000$ so I'm seeing if there's a way to solve it at a cost comparable to $d\times d$ SVD.
$A$,$B$ are positive-semi-definite and $C$ may have a few zeros.