I want to find the best parameters for a model given a set of measurements. The model has the function $y = a + b \cdot \frac{x-c}{x+c}$, where $a,b,c \in \mathbb{C}$ are the parameters that must be optimized and $ x \in \mathbb{C}$ is the model input and $ y \in \mathbb{C}$ is the model output. I have acquired a set of $N$ measurements with known $(x_i, y_i)$. Now I would like to find the best set of $(a, b, c)$ to match the measurements as close as possible.
So that would boil down to minimizing $f$, where
$$ f = \sum_i \left\lVert a + b \cdot \frac{x_i-c}{x_i+c} - y_i \right\rVert $$
No constraints are given on $(a, b, c)$.
I am currently a bit clueless about proceeding with this optimization problem. Is there a particular method that suits well for this?
Kind regards, Peter