Let's say I am given
$\left \{ \phi_{ij}, \mu_{ij} \mid 0 < \phi_{ij}, \mu_{ij} \in \mathbb{Q} \wedge i,j \in \{1,..,n\} \right \}$
and I want to find or approximate
$\alpha_{1},..,\alpha_{n}$
such that
$\left | \sum_{\forall i,j} (\phi_{ij} - \frac{\alpha_i}{\alpha_j}) * \mu_{ij} \right |$
is minimal. Is there any (hopefully computationally inexpensive) way to achieve this?