All Questions

Let $x_1, \dotsc, x_n \in \mathbb{R}^d$ and $\theta_1, \dotsc, \theta_n \in \mathbb{R}^d$ be vectors such that for every $k \in [n]$, the following inequality holds: $$ \langle x_k, \theta_k \rangle &...

This post is a variant on To cut a triangle into $n$ $p$-sided polygonal regions. Question: Given a positive integer $n$, a triangular region is to be cut into $n$ convex pieces so that the sum over ...

I have an optimization problem and was using a linear programming optimizer to find solutions. However, I find that past a certain size, the problem becomes "infeasible" and has no solutions....

Let $Q \subseteq R^n$ be a rational polyhedron and let $Q_I=Convexhull(Q \cap Z^n)$. By finite basis theorem, we have $Q=P+C$ for some rational polytope $P$ and finitely generated cone $C$ where $C=R_+...

I wonder if something similar to the following fact is known, and I would greatly appreciate any references. Let $t_1, t_2, \ldots, t_N$ be unit vectors in $\mathbb{R}^n$. Let $S$ denote the unit ...

I am trying to prove that a natural greedy algorithm solves the following instance of the set cover problem: for a set of elements $e\in U$ with a set of weights $w_e$, we define the cost of a subset ...