The following inequality constraint function is nonconvex \begin{equation} \frac{G_{ii}P_i}{\sum_{j=1,i \neq j} G_{ij} P_j + \sigma_i^2} \geq \gamma_0 \end{equation}
However, by applying function transformation, the constraint can be written as \begin{equation} -G_{ii}P_i + \gamma_0 \sum_{j=1,i \neq j} G_{ij} P_j + \gamma_0 \sigma_i^2 \leq 0 \end{equation} which is obviously a convex constraint in $p_i$ (more specifically an LP)
I am wondering why they are different? They are same equation, but one is non-convex and the other is convex.