Consider the following convex region $$ \{x\in \mathbb{R}^K: Ax\leq b \} $$ where $A$ is a known $m\times K$ matrix and $b$ is a known $m\times 1$ vector.
Let $x_i$ be the $i$-th element of $x$.
I want to find the minimum and maximum value of $x_i$ in the region (i.e., I want to find the projection of the region in the $i$-th dimension).
Which optimisation problem I should solve to get such min and max?