All Questions

Let $P$ be a convex polytope in $\mathbb{R}^d$ with $n$ vertices and $f$ facets. Let $\text{Proj}(P)$ denote the projection of $P$ into $\mathbb{R}^2$. Can $\text{Proj}(P)$ have more than $f$ facets? ...

Let $f=\mathbf{c}\cdot\mathbf{x}$ be the optimization objective function whose parameter vector $\mathbf{x}\in\mathbb{R}^n$ is subject to the following constraints in the very well-known linear-...

This problem is likely best described with the following picture: Given the discrete set of points $A$ (shown in blue), I wish to calculate the discrete set of points that are contained within the ...

Let $N$ be a finite subset of the naturals. Let $P$ be a set of subsets of $N$ such that: 1) $P\neq \varnothing$, 2) $\forall x\in P, |x| >1$, 3) $\forall x,y\in P,$ if $x\neq y$, then $x\not\...

I have a high-dimensional, non-empty polytope $Ax\geq b$ sitting inside the cube ($0\leq x_i \leq 1$). Is there any general theory or technique to show that this polytope contains an integer point, ...