Question related to optimization problems.
$$\mathrm{maximize} \sum\limits_{i=1}^{M}\log\left(1+f_i(\mathbf{x})\right)$$
$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\;\;\mathrm{subject}\, \mathrm{to}\;f_i(\mathbf{x})>\Gamma_i\,\forall\, i\in\{1, \dotsc, M\}$
Since we are maximizing a sum of increasing functions subject to a lower bound, is this problem feasible?
This kind of problem is often used in networking when the objective is maximize the sum rate subject to the individual rate of a user $i$.
It depends on how you define $f_i(x)$, if there are finite number of $x$ satisfy your constraints, then I think it's feasible. Because at least you can check every $x$ and find the maximum one.