Question

How would one prove that a linear combination of convex functions is also convex?

score 9.2k · Answer 1 · 2026-03-28 07:32:26

9.2k

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How would one prove that a linear combination of convex functions is also convex?

Published on 28 Mar 2026 - 7:32

score 92 · Answer 2 · 2026-03-26 06:25:27

92

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Approximate a convex body by polyhedron

Published on 26 Mar 2026 - 6:25

score 157 · Answer 3 · 2026-03-25 18:38:42

157

Views

Minkowski sum of duals

Published on 25 Mar 2026 - 18:38

score 297 · Answer 4 · 2026-03-26 17:33:31

297

Views

Prove or disprove that the set of probabilities $\{p \in \Delta^n \mid \mbox{Var}(X) \leq \alpha\}$ is a convex set.

Published on 26 Mar 2026 - 17:33

score 280 · Answer 5 · 2026-03-27 14:28:46

280

Views

Proof verification in constructive analysis

Published on 27 Mar 2026 - 14:28

score 61 · Answer 6 · 2026-03-26 09:42:19

61

Views

Quasiconvexity of a specific quartic bivariate polynomial family

Published on 26 Mar 2026 - 9:42

score 61 · Answer 7 · 2018-09-25 10:42:50

61

Views

Convexity of a multivariate linear equation

Published on 25 Sep 2018 - 10:42

score 128 · Answer 8 · 2018-09-25 11:05:13

128

Views

Hahn-Banach separation theorem where one of the sets is neither open nor closed.

Published on 25 Sep 2018 - 11:05

score 37 · Answer 9 · 2026-03-28 07:27:13

37

Views

Given the following two assumptions, How to conclude $\lim_{k \rightarrow \infty}|\nabla g_r(y^{k})|=0 \ $?

Published on 28 Mar 2026 - 7:27

score 313 · Answer 10 · 2026-03-25 05:05:42

313

Views

Convexity of expectation

Published on 25 Mar 2026 - 5:05

score 75 · Answer 11 · 2026-03-25 01:28:52

75

Views

Show that $\{p \in \Delta^n \mid b^T p + p^T Ap \leq \alpha\}$ is a convex set.

Published on 25 Mar 2026 - 1:28

score 3.6k · Answer 12 · 2018-09-26 03:11:18

3.6k

Views

Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex

Published on 26 Sep 2018 - 3:11

score 110 · Answer 13 · 2026-03-25 08:49:05

110

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Dual element of supporting function

Published on 25 Mar 2026 - 8:49

score 64 · Answer 14 · 2026-03-25 22:05:28

64

Views

Is $f:\mathbb R\to\mathbb R$ concave everywhere if, within each interval on the domain, $\exists$ a sub-interval s.t. $f$ is concave locally?

Published on 25 Mar 2026 - 22:05

score 896 · Answer 15 · 2026-03-27 21:44:37

896

Views

Identify the extreme points and extreme directions of $S = \{x : 4x_2 \geq x_1^2, x_1 +2x_2 + x_3 \leq 2\}$

Published on 27 Mar 2026 - 21:44

List Question

How would one prove that a linear combination of convex functions is also convex?

Approximate a convex body by polyhedron

Minkowski sum of duals

Prove or disprove that the set of probabilities $\{p \in \Delta^n \mid \mbox{Var}(X) \leq \alpha\}$ is a convex set.

Proof verification in constructive analysis

Quasiconvexity of a specific quartic bivariate polynomial family

Convexity of a multivariate linear equation

Hahn-Banach separation theorem where one of the sets is neither open nor closed.

Given the following two assumptions, How to conclude $\lim_{k \rightarrow \infty}|\nabla g_r(y^{k})|=0 \ $?

Convexity of expectation

Show that $\{p \in \Delta^n \mid b^T p + p^T Ap \leq \alpha\}$ is a convex set.

Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex

Dual element of supporting function

Is $f:\mathbb R\to\mathbb R$ concave everywhere if, within each interval on the domain, $\exists$ a sub-interval s.t. $f$ is concave locally?

Identify the extreme points and extreme directions of $S = \{x : 4x_2 \geq x_1^2, x_1 +2x_2 + x_3 \leq 2\}$

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