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Let $a_{i,j}$ and $b_{i,j}$ be real numbers for $i,j\in\{1,\ldots,m\}$. Let $z_k\in\{0,1\}$ for $k=1,\ldots,m$. Is there a common method of maximizing,

$f(z_1,\ldots,z_m)=\displaystyle\frac{\sum_{(i,j)} a_{i,j}z_iz_j}{\sum_{(i,j)} b_{i,j}z_iz_j}$

A resource directly related to this problem would be extremely helpful.

Joseph Zambrano
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  • Interesting problem. This seems to do the trick, I hope you have some access (otherwise, tell me, I will see what I can do) : http://www.sciencedirect.com/science/article/pii/S0167506008707362 – Vincent Sep 02 '16 at 09:58
  • @Vincent Unfortunately I do not, I will do some digging with the relevant terms mentioned. Thank you! – Joseph Zambrano Sep 02 '16 at 11:49

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