I have the following function:
$$f(x,y) = \min \left\{ x(1-y), -1+2y+\frac{y^2}{4(1+y)}, \frac{1}{5} -\frac{11}{5}x \right\}$$
and I would like to optimize this function where
$$0 < x < \frac{1}{11}, \qquad \frac{2(\sqrt{10} - 1)}{9} < y < 1$$
How do I go about this? How do I find the maximum? If it helps, I am trying to understand page 156 of this paper. I can't seem to get where the cubic polynomial comes into the picture? Thanks.