I want to ask how to derive the support function of the convex set (in $\mathbb{R}^2$) that is described as the intersection of
$x_1\leq \frac{3}{4}$, $x_2\leq \frac{3}{4}$, $x_1+x_2\leq 1$, and $x_1\geq 0$, $x_2\geq 0$.
I mean could you please suggest a general method? Thanks a lot.
Its the Gilbert–Johnson–Keerthi (GJK) algorithm, man, see here.