Question

The convex hull of a finite subset of $\Bbb{R}^2$ is the intersection of all closed half plane

score 364 · Answer 1 · 2021-05-05 18:36:14

364

Views

The convex hull of a finite subset of $\Bbb{R}^2$ is the intersection of all closed half plane

Published on 05 May 2021 - 18:36

score 233 · Answer 2 · 2021-05-05 23:48:25

233

Views

Number of vertices of 3D Zonotope in general position with all positive generators

Published on 05 May 2021 - 23:48

score 81 · Answer 3 · 2021-05-16 04:56:26

81

Views

Non-negative linear combination equal to sum of one component

Published on 16 May 2021 - 4:56

score 73 · Answer 4 · 2021-05-16 20:36:41

73

Views

Why does Radon's 8 theorem not work for $n+1$

Published on 16 May 2021 - 20:36

score 63 · Answer 5 · 2021-05-25 07:56:31

63

Views

Let $x_1,...,x_k \in \mathbb{R}^n$. Assume $0 \not\in conv\{x_1,...,x_k\}$. Show there is a $c\in \mathbb{R}^n$ s.t. $c^Tx_i \geq1$ for all $i\in[k]$.

Published on 25 May 2021 - 7:56

score 364 · Answer 6 · 2021-05-30 09:51:33

364

Views

On computing the convex hull

Published on 30 May 2021 - 9:51

score 131 · Answer 7 · 2021-06-01 17:41:22

131

Views

$K= \overline{conv(E)}$ iff for every continuous linear functional $f:X\rightarrow \mathbb{R} $ we have $ \sup_{x \in K}f(x)= \sup_{x \in E}f(x)$

Published on 01 Jun 2021 - 17:41

score 33 · Answer 8 · 2021-06-06 08:23:17

33

Views

Let $A_1,\dots,A_k \subset \mathbb{R}^n$. If $x \in \text{conv}(A_1+…+A_k)$, then $x \in \text{conv}(A_1’+…+A_k’)$, with finite $A_i’ \subset A_i$.

Published on 06 Jun 2021 - 8:23

score 45 · Answer 9 · 2021-06-06 08:41:43

45

Views

Let $K,L$ be convex bodies in $\mathbb{R}^n$ s.t. $(K \cup L)$ is convex. If $x \in K, y \in L$, then $[x,y] \cap (K \cap L) \neq \emptyset$.

Published on 06 Jun 2021 - 8:41

score 94 · Answer 10 · 2021-06-17 23:37:43

94

Views

Prove that a set is the convex hull of another set

Published on 17 Jun 2021 - 23:37

score 95 · Answer 11 · 2026-03-25 11:13:41

95

Views

Perron root of convex combination of nonnegative matrices

Published on 25 Mar 2026 - 11:13

score 125 · Answer 12 · 2026-03-26 06:05:38

125

Views

How can I solve the problem of convex hull

Published on 26 Mar 2026 - 6:05

score 141 · Answer 13 · 2021-07-12 14:43:42

141

Views

McCormick envelopes

Published on 12 Jul 2021 - 14:43

score 95 · Answer 14 · 2021-07-18 01:08:14

95

Views

How do I determine the lattice points of the convex hull of a set of {0,1}^n points?

Published on 18 Jul 2021 - 1:08

score 327 · Answer 15 · 2021-07-20 13:29:54

327

Views

Covering of a polytope by balls with midpoints at the vertices

Published on 20 Jul 2021 - 13:29

List Question

The convex hull of a finite subset of $\Bbb{R}^2$ is the intersection of all closed half plane

Number of vertices of 3D Zonotope in general position with all positive generators

Non-negative linear combination equal to sum of one component

Why does Radon's 8 theorem not work for $n+1$

Let $x_1,...,x_k \in \mathbb{R}^n$. Assume $0 \not\in conv\{x_1,...,x_k\}$. Show there is a $c\in \mathbb{R}^n$ s.t. $c^Tx_i \geq1$ for all $i\in[k]$.

On computing the convex hull

$K= \overline{conv(E)}$ iff for every continuous linear functional $f:X\rightarrow \mathbb{R} $ we have $ \sup_{x \in K}f(x)= \sup_{x \in E}f(x)$

Let $A_1,\dots,A_k \subset \mathbb{R}^n$. If $x \in \text{conv}(A_1+…+A_k)$, then $x \in \text{conv}(A_1’+…+A_k’)$, with finite $A_i’ \subset A_i$.

Let $K,L$ be convex bodies in $\mathbb{R}^n$ s.t. $(K \cup L)$ is convex. If $x \in K, y \in L$, then $[x,y] \cap (K \cap L) \neq \emptyset$.

Prove that a set is the convex hull of another set

Perron root of convex combination of nonnegative matrices

How can I solve the problem of convex hull

McCormick envelopes

How do I determine the lattice points of the convex hull of a set of {0,1}^n points?

Covering of a polytope by balls with midpoints at the vertices

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