**Problem:** Let $a_{i,j}$, $b_{i,j}\in\mathbb{R}$ for all $(i,j)\in\left[m\right]^2$ such that $a_{i,j}=a_{j,i}$ and $b_{i,j}=b_{j,i}$. Let $z_k\in\{0,1\}$ for $k\in\left[m\right]$. We wish to maximize,

$f(z)=\displaystyle\frac{\displaystyle\sum_{(i,j)}a_{i,j}z_iz_j}{\displaystyle\sum_{(i,j)}b_{i,j}z_iz_j}$

Note that the numerator and denominator are assumed to be strictly positive.

**Thoughts:** I am aware of general notions of linear fractional programming. However, I am unsure whether the $z_iz_j$ terms/optimization over the hypercube will drastically change the availability of methods.