I want to solve the following optimisation problem in $W_0 \in \{0,1\}^{m \times k}$
$$\begin{array}{ll} \text{minimize} & \left\| \left\lfloor \frac 1t X_{0} W_{0} \right\rfloor - X_{1} \right\|_F^2\end{array}$$
where $t \in \mathbb R \setminus \{0\}$, $X_1 \in \{0,1\}^{n \times k}$ and $X_0 \in \{0,1\}^{n \times m}$ are given.
I am not sure how to use binary quadratic programming for this problem. Any other suggestion would be greatly appreciated. Thanks in advance.