I have a known matrix, $H$ of size $U\times B$. The optimization variable is $D$ of same size, which is binary
Now I have $$S_u=\frac{\sum\limits_{b=1}^{B} D_{u,b}H_{u,b}}{\sum\limits_{b=1}^{B}H_{u,b}-\sum\limits_{b=1}^{B} D_{u,b}H_{u,b}},\quad \forall u\in\{1,\cdots, U\}$$ and I want to maximize $\sum\limits_{u=1}^US_u$.
UPDATE:
with $b_\min\le \sum_{b=1}^B D_{u,b}\le b_\max, \forall u$ and $\sum_{u=1}^{U}D_{u,b}\le u_\max, \forall b$
Can I perform some alternative formulation so that the function becomes convex, or any convex approximation?
EDIT:
The denominator is strictly non-negative. The first or positive part of the denominator denotes the case where $D_{u,b}=1, \forall b, b=1,\cdots, B$
Also, the elements in $H$ are non-negative.