I have a function of the form $f(x,y) = \frac{x}{c+y}$ where $c$ is a positive constant and $d \ge x, y \ge 0$. I would like to find a convex upper-bound for this function. Is there a principled way for doing this? How about if the upper-bound has to be convex and piecewise linear? Is there a way to find the optimal upper-bound in terms of the number of piecewise linear terms?