How could one solve the following least-squares problem with [Frobenius Norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm) and diagonal matrix constraint?

$$\hat{S} := \arg \min\_{S} \left\| Y - XUSV^T \right\|\_{F}^{2}$$

where the $S$ is a diagonal matrix and $U,V$ are column-orthogonal matrix. Is there any fast algorithm?