I have the following optimization problem
\begin{equation} \begin{aligned} \max_{\mathbf{x}} & \ |d-\sum_{n=1}^{N}\frac{c_n}{f_n+x_n} |^2 \\ \quad \text{subject to} \quad & \sum_{n=1}^{N} \frac{|a_n|^2 Re(x_n)}{|f_n+x_n|^2} = 0. \end{aligned} \end{equation} where $d$ is a complex scalar, $\mathbf{f}=[f_1,...,f_N]$, $\mathbf{c}=[c_1,...,c_N]$ and $\mathbf{a}=[a_1,...,a_N]$ are complex vectors. Can you please give me some ideas on how to solve it ? I was thinking to consider
\begin{equation} y_n=\frac{1}{f_n+x_n}, \quad \forall n \in \{0\,...,N\} \end{equation}
and then to transform it to linear programming. Is it possible ?
Thank you