Question

Let $C \subset \mathbb{R}^n$ be a given set. Show that the set $C^o = {\{y \in \mathbb{R}^n : y^Tx \le 0, \forall x \in C\}}$ is convex.

score 39 · Answer 1 · 2026-03-28 17:41:10

39

Views

Let $C \subset \mathbb{R}^n$ be a given set. Show that the set $C^o = {\{y \in \mathbb{R}^n : y^Tx \le 0, \forall x \in C\}}$ is convex.

Published on 28 Mar 2026 - 17:41

score 357 · Answer 2 · 2026-03-25 07:44:50

357

Views

When does Brunn-Minkowski inequatily $(m(A+B))^{1/d} \geqslant (m(A))^{1/d} + (m(B))^{1/d}$ become equality?

Published on 25 Mar 2026 - 7:44

score 12.7k · Answer 3 · 2018-10-19 08:29:31

12.7k

Views

Is a convex function always continuous?

Published on 19 Oct 2018 - 8:29

score 159 · Answer 4 · 2018-10-19 09:13:34

159

Views

Show that the given set is convex for $a,b \in \mathbb{R}$

Published on 19 Oct 2018 - 9:13

score 40 · Answer 5 · 2026-03-28 15:59:37

Is the set $\{a \in \mathbb{R}^k : p(0) = 1, |p(t)| \le 1$ for $0 \le t \le 1 \},$ where $p(t) = a_1 + a_2t + ... + a_kt^{k-1}$ convex?

score 153 · Answer 6 · 2018-10-19 22:15:50

153

Views

A problem regarding Convex Hull.

Published on 19 Oct 2018 - 22:15

score 104 · Answer 7 · 2026-03-27 13:25:47

104

Views

Exhaustion in compact convex (totally geodesic) subsets of a complete manifold

Published on 27 Mar 2026 - 13:25

score 62 · Answer 8 · 2026-03-28 02:42:58

62

Views

Convex polyhedron: Show $B$ is an extremal point and $A$ is not

Published on 28 Mar 2026 - 2:42

score 1.4k · Answer 9 · 2018-10-20 15:19:30

1.4k

Views

How to prove that $e^{ax}$ is convex?

Published on 20 Oct 2018 - 15:19

score 706 · Answer 10 · 2026-03-27 11:48:05

706

Views

Proof of convexity of linear least squares with convexity properties

Published on 27 Mar 2026 - 11:48

score 144 · Answer 11 · 2026-03-25 20:17:58

144

Views

Calculating the Sub Differential Through Proximal Operator / Mapping

Published on 25 Mar 2026 - 20:17

score 62 · Answer 12 · 2018-10-21 18:48:28

62

Views

Prove V is a convex set

Published on 21 Oct 2018 - 18:48

score 385 · Answer 13 · 2018-10-22 01:24:56

385

Views

Boyd & Vandenberghe, problem 3.49 (c) — proving that a function is log-concave

Published on 22 Oct 2018 - 1:24

score 27 · Answer 14 · 2018-10-22 07:37:23

27

Views

Writting elements in the boundary of a set as combination of other elements

Published on 22 Oct 2018 - 7:37

score 69 · Answer 15 · 2018-10-22 13:12:58

69

Views

Prove this function is strictly convex

Published on 22 Oct 2018 - 13:12

List Question

Let $C \subset \mathbb{R}^n$ be a given set. Show that the set $C^o = {\{y \in \mathbb{R}^n : y^Tx \le 0, \forall x \in C\}}$ is convex.

When does Brunn-Minkowski inequatily $(m(A+B))^{1/d} \geqslant (m(A))^{1/d} + (m(B))^{1/d}$ become equality?

Is a convex function always continuous?

Show that the given set is convex for $a,b \in \mathbb{R}$

Is the set $\{a \in \mathbb{R}^k : p(0) = 1, |p(t)| \le 1$ for $0 \le t \le 1 \},$ where $p(t) = a_1 + a_2t + ... + a_kt^{k-1}$ convex?

A problem regarding Convex Hull.

Exhaustion in compact convex (totally geodesic) subsets of a complete manifold

Convex polyhedron: Show $B$ is an extremal point and $A$ is not

How to prove that $e^{ax}$ is convex?

Proof of convexity of linear least squares with convexity properties

Calculating the Sub Differential Through Proximal Operator / Mapping

Prove V is a convex set

Boyd & Vandenberghe, problem 3.49 (c) — proving that a function is log-concave

Writting elements in the boundary of a set as combination of other elements

Prove this function is strictly convex

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