# Questions tagged [convex-hulls]

The convex hull of a set $X$ of points in a Euclidean space is the smallest convex set that contains $X$.

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### How to apply Hahn-Banach to the convex hull?

I am trying to understand the proof of Lemma 4.1.2 in Michel Talagrand's publication from 1995 on concentration inequalities (see below for the precise question statement): A bit of context: ...
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### Compute the edge-skeleton of a polytope given by its vertices

Let $P$ be a polytope given by a vertex description, i.e., $P=conv(\{x_1,\ldots,x_m\})\subset\mathbb{R}^n$. Is there an efficient (i.e., not relying on Linear Programming) algorithm to compute the ...
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### Convex hull of piece-wise linear functions

Let $K>1$ be a positive integer. Consider a function class $$\mathcal{F}_K:=\Big\{\max_{1\leq k\leq K} a_k^\top x + b_k:\ ||a_k||\leq 1, |b_k|\leq 1, \forall 1\leq k\leq K \Big\}$$ on some compact ...
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### Where to submit a new convex hull algorithm?

Recently, I devised a new convex hull algorithm. Is there any forum where I can submit my work?
### Convex hull of $k$ random points
Suppose we have $k$ realizations of a random variable uniformly distributed over the unit cube $[0,1]^n$. What is the probability that their convex hull has all of the $k$ points as extreme points? ...
Let $X$ be complete $\mathop{CAT}(0)$-space and $K\subset X$ be a compact subset. Is it true that convex hull of $K$ is compact? Comments: Convex hull of $K$ = intersection of all closed convex sets ...