My optimisation problem has a constraint in the form
\begin{equation} \begin{array}{*{35}{l}} \text{}\hspace{16.5mm}\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\sum_{u=1}^U d_{u,C}L_{u}=\psi_1:\psi_2:\cdots:\psi_C \end{array} \end{equation}
This nonlinear and makes the problem even more complex.
Here $L_{u}$ and $\psi_{c}$ are known parameters.
I will be satisfied with approximate proportional relation, e..g, C4 can be
$\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\sum_{u=1}^U d_{u,C}L_{u}\approx\psi_1:\psi_2:\cdots:\psi_C$
How can I deal with this nonlinear constraint?