Question

Separation properties of convex set in the n-dimensional Euclidean space

score 108 · Answer 1 · 2026-04-01 15:42:19

108

Views

Separation properties of convex set in the n-dimensional Euclidean space

Published on 01 Apr 2026 - 15:42

score 28 · Answer 2 · 2026-03-25 06:01:27

28

Views

Language to describe that a multivariate function is convex with respect to only certain variables

Published on 25 Mar 2026 - 6:01

score 207 · Answer 3 · 2026-03-26 12:50:38

207

Views

Let $f_1$,$f_2$ be two convex functions on $R^n$. Show $\max[f_1(x),f_2(x)]$ is a convex function as well

Published on 26 Mar 2026 - 12:50

score 326 · Answer 4 · 2026-03-26 14:23:06

326

Views

Assume an LP has 2 optimal solutions $u$ and $v$. Show for any t in [0,1] that $tu+(1-t)v$ is also optimal

Published on 26 Mar 2026 - 14:23

score 50 · Answer 5 · 2026-04-02 23:16:58

50

Views

Prove $e^{e^{e^x}}$ is convex on $\mathbb{R}$.

Published on 02 Apr 2026 - 23:16

score 218 · Answer 6 · 2026-03-26 14:22:56

218

Views

Is the union of any set of faces of a closed convex set closed?

Published on 26 Mar 2026 - 14:22

score 48 · Answer 7 · 2019-09-27 15:49:51

48

Views

Let $A\subseteq S^{d-1} = \{x\in \mathbb{R}^{d}: ||x||=1 \}$ be a subset of any unit sphere. Let $E \triangleq \{x\in \mathbb{R}: ||x||<1 \} \cup A$

Published on 27 Sep 2019 - 15:49

score 52 · Answer 8 · 2026-03-30 12:58:50

52

Views

If f is a convex function defined over the set $[a,b]$ then it achieves the maximum at one of the boundry points.

Published on 30 Mar 2026 - 12:58

score 40 · Answer 9 · 2026-03-30 01:51:36

40

Views

What can one say about the set of points where a function is lower semicontinuous?

Published on 30 Mar 2026 - 1:51

score 2.1k · Answer 10 · 2019-09-29 18:14:34

2.1k

Views

Danskins' theorem

Published on 29 Sep 2019 - 18:14

score 360 · Answer 11 · 2019-09-30 01:41:42

360

Views

Is a positively homogeneous convex function lower semi-continuous?

Published on 30 Sep 2019 - 1:41

score 35 · Answer 12 · 2019-09-30 03:55:57

35

Views

Convex optimization with larger feasible set has more solutions, is this correct?

Published on 30 Sep 2019 - 3:55

score 88 · Answer 13 · 2019-09-30 09:32:00

88

Views

Proving Caratheodory theorem by induction on the dimension

Published on 30 Sep 2019 - 9:32

score 61 · Answer 14 · 2019-09-30 13:02:59

61

Views

$f$ Concave function such as $f(0)=0$

Published on 30 Sep 2019 - 13:02

score 71 · Answer 15 · 2019-09-30 14:58:53

71

Views

Why is $(X-a)^{+}$ an increasing convex function?

Published on 30 Sep 2019 - 14:58

List Question

Separation properties of convex set in the n-dimensional Euclidean space

Language to describe that a multivariate function is convex with respect to only certain variables

Let $f_1$,$f_2$ be two convex functions on $R^n$. Show $\max[f_1(x),f_2(x)]$ is a convex function as well

Assume an LP has 2 optimal solutions $u$ and $v$. Show for any t in [0,1] that $tu+(1-t)v$ is also optimal

Prove $e^{e^{e^x}}$ is convex on $\mathbb{R}$.

Is the union of any set of faces of a closed convex set closed?

Let $A\subseteq S^{d-1} = \{x\in \mathbb{R}^{d}: ||x||=1 \}$ be a subset of any unit sphere. Let $E \triangleq \{x\in \mathbb{R}: ||x||<1 \} \cup A$

If f is a convex function defined over the set $[a,b]$ then it achieves the maximum at one of the boundry points.

What can one say about the set of points where a function is lower semicontinuous?

Danskins' theorem

Is a positively homogeneous convex function lower semi-continuous?

Convex optimization with larger feasible set has more solutions, is this correct?

Proving Caratheodory theorem by induction on the dimension

$f$ Concave function such as $f(0)=0$

Why is $(X-a)^{+}$ an increasing convex function?

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