I have the following constraint for the optimization problem in hand:
$$\frac{b_k}{\log_2 \left(1 + \frac{p_k \alpha_k}{\sum_{j \neq k} p_j \alpha_j + \sum_n \sum_l \Xi_{n,l,k} 2^{-2 v_{n,l}}} \right)} + 2 \frac{\sum_n \sum_l v_{n,l} }{C_F} \leq \epsilon$$
where the variables are $v_{n,l}$, $p_k$, $p_j, \; j \neq k$. The constants are $\alpha_k$, $\alpha_j$, $b_k$, $C_F$, $\Xi_{n,l,k}$.
The constraint is non-convex in $\{v_{n,l}, p_k, p_j, \; j \neq k\}$. I am looking solve the problem with sucessive convex approximation approach.
I need some suggestion on feasibilty of the problem in terms of it if its possible to have a convex approximation for the above constraint and or suggest some method to solve it.