Question

Linear programming: What is the set of gradients of the objective function for which a given extreme point of the feasible region is optimal?

score 596 · Answer 1 · 2021-03-27 12:25:15

596

Views

Linear programming: What is the set of gradients of the objective function for which a given extreme point of the feasible region is optimal?

Published on 27 Mar 2021 - 12:25

score 228 · Answer 2 · 2026-02-23 10:49:44

228

Views

Find out the convex hull of the set $\left\{\pm \mathbf{u} \mathbf{u}^{T} \mid\|\mathbf{u}\|=1\right\}$ in a compact form ($u$ is a n-d vector)

Published on 23 Feb 2026 - 10:49

score 196 · Answer 3 · 2021-03-30 15:53:42

196

Views

How many points are required to represent the unit ball in the $\ell_{\infty}$-norm as a convex hull?

Published on 30 Mar 2021 - 15:53

score 48 · Answer 4 · 2021-04-02 14:49:07

48

Views

Given $K$ points in the $N$-simplex, when is there a unique $M$-polytope that contains the $K$ points?

Published on 02 Apr 2021 - 14:49

score 43 · Answer 5 · 2021-04-04 21:13:38

43

Views

Convexity of a configuration of $n$ points

Published on 04 Apr 2021 - 21:13

score 24 · Answer 6 · 2021-04-15 15:17:30

24

Views

extreme points on cumulative sequence.

Published on 15 Apr 2021 - 15:17

score 57 · Answer 7 · 2021-04-16 19:49:01

57

Views

analytical form for extreme points of polynomial on intervals.

Published on 16 Apr 2021 - 19:49

score 86 · Answer 8 · 2021-04-16 23:00:49

86

Views

Compact set and simplex

Published on 16 Apr 2021 - 23:00

score 629 · Answer 9 · 2021-04-18 06:46:29

629

Views

Proving the affine hull definition from the intersection of affine spaces (Rockafellar's Convex Analysis)

Published on 18 Apr 2021 - 6:46

score 209 · Answer 10 · 2021-04-20 23:50:13

209

Views

$\|x_0 − y_0\| = \operatorname{dist}(A, B)$

Published on 20 Apr 2021 - 23:50

score 229 · Answer 11 · 2021-04-21 16:34:57

229

Views

Derive an algorithm of convex hulls intersection with $O(n)$ time

Published on 21 Apr 2021 - 16:34

score 72 · Answer 12 · 2021-04-22 12:39:59

72

Views

Number of connected components of the polynomially convex hull of a compact $K\subset\Bbb C^n$

Published on 22 Apr 2021 - 12:39

score 443 · Answer 13 · 2021-04-22 18:45:21

443

Views

Proof the conic hull of a finite set of vectors is closed

Published on 22 Apr 2021 - 18:45

score 295 · Answer 14 · 2021-04-27 10:59:12

295

Views

Supporting hyperplane

Published on 27 Apr 2021 - 10:59

score 94 · Answer 15 · 2021-05-01 20:38:36

94

Views

Proving that a convex cone doesn't contain the negative of any point in the cone

Published on 01 May 2021 - 20:38

List Question

Linear programming: What is the set of gradients of the objective function for which a given extreme point of the feasible region is optimal?

Find out the convex hull of the set $\left\{\pm \mathbf{u} \mathbf{u}^{T} \mid\|\mathbf{u}\|=1\right\}$ in a compact form ($u$ is a n-d vector)

How many points are required to represent the unit ball in the $\ell_{\infty}$-norm as a convex hull?

Given $K$ points in the $N$-simplex, when is there a unique $M$-polytope that contains the $K$ points?

Convexity of a configuration of $n$ points

extreme points on cumulative sequence.

analytical form for extreme points of polynomial on intervals.

Compact set and simplex

Proving the affine hull definition from the intersection of affine spaces (Rockafellar's Convex Analysis)

$\|x_0 − y_0\| = \operatorname{dist}(A, B)$

Derive an algorithm of convex hulls intersection with $O(n)$ time

Number of connected components of the polynomially convex hull of a compact $K\subset\Bbb C^n$

Proof the conic hull of a finite set of vectors is closed

Supporting hyperplane

Proving that a convex cone doesn't contain the negative of any point in the cone

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