Question

How to prove that continuous convex functional on normed vector space must be lower bounded by some continuous affine functional?

score 264 · Answer 1 · 2026-05-07 13:38:50

264

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How to prove that continuous convex functional on normed vector space must be lower bounded by some continuous affine functional?

Published on 07 May 2026 - 13:38

score 1.1k · Answer 2 · 2026-05-10 18:26:16

1.1k

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Product of two polytopes is a polytope

Published on 10 May 2026 - 18:26

score 70 · Answer 3 · 2026-05-10 18:29:06

70

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Permutahedron of three vectors (1,1,0,0), (−1,1,0,0), (−1,−1,0,0).

Published on 10 May 2026 - 18:29

score 1.1k · Answer 4 · 2026-04-09 22:57:15

1.1k

Views

How to prove normal cones are closed?

Published on 09 Apr 2026 - 22:57

score 89 · Answer 5 · 2026-04-14 08:45:46

89

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Sums of unit vectors contained in a half-space

Published on 14 Apr 2026 - 8:45

score 142 · Answer 6 · 2026-04-12 13:04:14

142

Views

How can I prove that $\mathbb{S}_{+}^n$ is a closed and convex set?

Published on 12 Apr 2026 - 13:04

score 12.2k · Answer 7 · 2026-05-10 19:45:10

12.2k

Views

What is the difference between a unit simplex and a probability simplex?

Published on 10 May 2026 - 19:45

score 73 · Answer 8 · 2026-04-15 18:30:53

73

Views

Maximize $b^Tx$ subject to $x \in C(a) := \{x \in \mathbb R^p | \|a+x\|_2 \le r,\;\|x\|_\infty \le \epsilon\}$

Published on 15 Apr 2026 - 18:30

score 63 · Answer 9 · 2026-05-10 13:45:01

63

Views

A theorem about convex function

Published on 10 May 2026 - 13:45

score 491 · Answer 10 · 2026-05-10 18:27:52

491

Views

Prove that 0 is in the convex hull of points chosen from each orthant

Published on 10 May 2026 - 18:27

score 322 · Answer 11 · 2026-04-15 17:44:39

322

Views

Normal of a supporting hyperplane contained in the normal cone of a vertex

Published on 15 Apr 2026 - 17:44

score 37 · Answer 12 · 2026-04-13 03:26:59

37

Views

Quasiconvexity + X implies convexity

Published on 13 Apr 2026 - 3:26

score 48 · Answer 13 · 2026-04-14 19:20:27

48

Views

Polytopes given by affine relations of their vertices

Published on 14 Apr 2026 - 19:20

score 111 · Answer 14 · 2026-04-14 06:55:23

111

Views

Where to find some subset of Khovanskii's 15 proofs of the BKK theorem?

Published on 14 Apr 2026 - 6:55

score 1.8k · Answer 15 · 2026-05-10 15:52:10

1.8k

Views

Algorithms for projecting a point onto the convex hull spanned by a set of vectors

Published on 10 May 2026 - 15:52

List Question

How to prove that continuous convex functional on normed vector space must be lower bounded by some continuous affine functional?

Product of two polytopes is a polytope

Permutahedron of three vectors (1,1,0,0), (−1,1,0,0), (−1,−1,0,0).

How to prove normal cones are closed?

Sums of unit vectors contained in a half-space

How can I prove that $\mathbb{S}_{+}^n$ is a closed and convex set?

What is the difference between a unit simplex and a probability simplex?

Maximize $b^Tx$ subject to $x \in C(a) := \{x \in \mathbb R^p | \|a+x\|_2 \le r,\;\|x\|_\infty \le \epsilon\}$

A theorem about convex function

Prove that 0 is in the convex hull of points chosen from each orthant

Normal of a supporting hyperplane contained in the normal cone of a vertex

Quasiconvexity + X implies convexity

Polytopes given by affine relations of their vertices

Where to find some subset of Khovanskii's 15 proofs of the BKK theorem?

Algorithms for projecting a point onto the convex hull spanned by a set of vectors

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