I have a linear optimization problem where the cost function is $ay - bx$. The variables are $(x, y)$. However, for one of the constraints, I have $\log_2 \frac{cx}{c^2 x + c(1 - y)(1 - c)} \geq \delta$. Note that the $x$ and $y$ are discrete here. The rest of the constraints are linear. I was wondering how can I find $x$ and $y$ that minimizes the cost function?
I have tried two approaches:
I have tried to expand the $\log_2$ with the Taylor series and approximate with only a linear component. But the error, in this case, is really high
In the second step, I tried to check if the cost function was convex or not. But as you can see the cost function is linear in $x$, and if I try to compute the second derivative (using central difference), it will result in 0.
So, what approach should I follow?