Question

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

score 9.2k · Answer 1 · 2026-04-13 00:13:34

9.2k

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

Published on 13 Apr 2026 - 0:13

score 95 · Answer 2 · 2026-05-11 03:02:35

95

Views

Approximate a convex body by polyhedron

Published on 11 May 2026 - 3:02

score 163 · Answer 3 · 2026-05-14 00:31:38

163

Views

Minkowski sum of duals

Published on 14 May 2026 - 0:31

score 299 · Answer 4 · 2026-04-16 07:30:59

299

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 16 Apr 2026 - 7:30

score 281 · Answer 5 · 2026-05-10 13:45:10

281

Views

Proof verification in constructive analysis

Published on 10 May 2026 - 13:45

score 64 · Answer 6 · 2026-05-11 03:10:21

64

Views

Quasiconvexity of a specific quartic bivariate polynomial family

Published on 11 May 2026 - 3:10

score 64 · Answer 7 · 2026-04-10 05:49:10

64

Views

Convexity of a multivariate linear equation

Published on 10 Apr 2026 - 5:49

score 131 · Answer 8 · 2026-04-15 14:19:34

131

Views

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

Published on 15 Apr 2026 - 14:19

score 38 · Answer 9 · 2026-04-14 18:19:13

38

Views

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

Published on 14 Apr 2026 - 18:19

score 318 · Answer 10 · 2026-05-14 12:47:11

318

Views

Convexity of expectation

Published on 14 May 2026 - 12:47

score 77 · Answer 11 · 2026-05-10 15:09:53

77

Views

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

Published on 10 May 2026 - 15:09

score 3.6k · Answer 12 · 2026-04-16 00:43:02

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 16 Apr 2026 - 0:43

score 120 · Answer 13 · 2026-05-16 00:55:58

120

Views

Dual element of supporting function

Published on 16 May 2026 - 0:55

score 67 · Answer 14 · 2026-05-10 20:44:04

67

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 10 May 2026 - 20:44

score 898 · Answer 15 · 2026-04-16 21:34:27

898

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 16 Apr 2026 - 21:34

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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