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This is just an NLP (Non-Linear Programming) model. You can rewrite it as: $$\begin{align}\min \>& Z \\ & \sum_i w_i = 1 \\ & \sum_i f_i(w_i\cdot Z)\ge k\cdot Z \\ & w_i \in [0,1] \end{align}$$ Getting rid of a division is always a good idea. If we can assume $Z\gt0$, then a slightly different formulation can look like: $$\begin{align}\...


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