Question

In resticted domain , Applying the Cauchy-Schwarz's inequality

score 77 · Answer 1 · 2026-03-22 12:13:21

77

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In resticted domain , Applying the Cauchy-Schwarz's inequality

Published on 22 Mar 2026 - 12:13

score 86 · Answer 2 · 2026-03-23 21:04:48

86

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Concave function - Generic proof

Published on 23 Mar 2026 - 21:04

score 116 · Answer 3 · 2026-03-22 18:18:37

116

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how to maximize $f(x,y)=\frac{x+y-2}{xy}$?

Published on 22 Mar 2026 - 18:18

score 138 · Answer 4 · 2026-03-22 15:27:12

138

Views

Proving $\frac{B_1B_2}{A_1A_3}+ \frac{B_2B_3}{A_2A_4}+...+\frac{B_nB_1}{A_nA_2}>1$

Published on 22 Mar 2026 - 15:27

score 85 · Answer 5 · 2026-03-23 08:46:39

85

Views

How to tranform the quasilinear constraint into convex or affine constraint?

Published on 23 Mar 2026 - 8:46

score 126 · Answer 6 · 2026-03-22 15:34:14

126

Views

How to show that if $f$ is a convex function, then the limit $\underset{t \rightarrow 0^+}{lim}\frac{f(x+ty)-f(x)}{t}$ exists?

Published on 22 Mar 2026 - 15:34

score 94 · Answer 7 · 2026-03-23 09:08:39

94

Views

Mid-point convexity and convexity

Published on 23 Mar 2026 - 9:08

score 201 · Answer 8 · 2026-03-22 21:30:10

201

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If $f$ is continuous and $f(\frac{x+y}{2})\leq \frac{f(x)+f(y)}2$ for all $x , y \in (a,b)$, prove that $f$ is convex.

Published on 22 Mar 2026 - 21:30

score 128 · Answer 9 · 2026-03-22 20:15:26

128

Views

Convexity of a function (volume-to-area ratio)

Published on 22 Mar 2026 - 20:15

score 107 · Answer 10 · 2026-03-23 09:48:31

107

Views

Proving $\sin 2x \geq x$, for $x \in \left[0, \frac{\pi}{4}\right]$

Published on 23 Mar 2026 - 9:48

score 266 · Answer 11 · 2026-03-21 21:53:33

266

Views

Showing that $x \mapsto |x|^p$ is strictly mid-point convex for $2 \leq p < \infty$

Published on 21 Mar 2026 - 21:53

score 101 · Answer 12 · 2026-03-17 09:07:09

101

Views

Proof of Convexity by Contradiciton

Published on 17 Mar 2026 - 9:07

score 75 · Answer 13 · 2026-03-20 03:54:43

75

Views

Non-convex objective function + (non-convex constraint function vs. convex constraint function)

Published on 20 Mar 2026 - 3:54

score 35 · Answer 14 · 2026-03-17 04:51:15

35

Views

Inequality involving Weibull distribution

Published on 17 Mar 2026 - 4:51

score 125 · Answer 15 · 2026-03-25 00:52:00

125

Views

Convexity of $x^{2q}$ implies $\mathbb{E} \big[ \left(X-X^{'}\right)^{2q} \big]\leq 2^{2q-1} \left( \mathbb{E}X^{2q}+ \mathbb{E}X^{'2q} \right) $

Published on 25 Mar 2026 - 0:52

List Question

In resticted domain , Applying the Cauchy-Schwarz's inequality

Concave function - Generic proof

how to maximize $f(x,y)=\frac{x+y-2}{xy}$?

Proving $\frac{B_1B_2}{A_1A_3}+ \frac{B_2B_3}{A_2A_4}+...+\frac{B_nB_1}{A_nA_2}>1$

How to tranform the quasilinear constraint into convex or affine constraint?

How to show that if $f$ is a convex function, then the limit $\underset{t \rightarrow 0^+}{lim}\frac{f(x+ty)-f(x)}{t}$ exists?

Mid-point convexity and convexity

If $f$ is continuous and $f(\frac{x+y}{2})\leq \frac{f(x)+f(y)}2$ for all $x , y \in (a,b)$, prove that $f$ is convex.

Convexity of a function (volume-to-area ratio)

Proving $\sin 2x \geq x$, for $x \in \left[0, \frac{\pi}{4}\right]$

Showing that $x \mapsto |x|^p$ is strictly mid-point convex for $2 \leq p < \infty$

Proof of Convexity by Contradiciton

Non-convex objective function + (non-convex constraint function vs. convex constraint function)

Inequality involving Weibull distribution

Convexity of $x^{2q}$ implies $\mathbb{E} \big[ \left(X-X^{'}\right)^{2q} \big]\leq 2^{2q-1} \left( \mathbb{E}X^{2q}+ \mathbb{E}X^{'2q} \right) $

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