Given a matrix $Y$, a symmetric matrix $L$ and a binary matrix $B$, I would like to solve an optimization problem of the form
$$ \min_{X} \quad \operatorname{trace} \left( X^T L X \right) \quad\quad \text{s.t.} \quad \|B\circ X-Y\|_{\text{F}} \leq \epsilon $$
where $\circ$ denotes the Hadamard product (a.k.a., element-wise product) and the norm is the Frobenius norm. How to solve this optimization problem?