I'm modeling a physical system and I've ended up with a term (sum of ratios of square of polar function's derivative to the original function) I would like to maximize in order to optimize the performance of the system:
$\sum^{n}_{i=1}\frac{[f_{i}'(\theta)]^{2}}{f_{i}(\theta)}$
where the polar functions $f(\theta)$ model a physical phenomenon which makes them necessarily belong to the class of functions $0 \lt f(\theta) \le 1 $. Since the sum is always positive, a simpler problem to start with would be to maximize each term - but even with that, I don't even know where to begin (I'm an engineer, not a mathematician). I do have further restrictions on the function including some parameterizations if it helps, but I am also curious if there's a general approach that could be used.