Question

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

score 84 · Answer 1 · 2026-04-29 12:18:10

84

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

Published on 29 Apr 2026 - 12:18

score 94 · Answer 2 · 2026-04-29 12:28:07

94

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Concave function - Generic proof

Published on 29 Apr 2026 - 12:28

score 121 · Answer 3 · 2026-05-10 15:27:30

121

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

Published on 10 May 2026 - 15:27

score 143 · Answer 4 · 2026-05-10 15:43:30

143

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 10 May 2026 - 15:43

score 93 · Answer 5 · 2026-04-29 12:44:18

93

Views

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

Published on 29 Apr 2026 - 12:44

score 133 · Answer 6 · 2026-05-10 12:02:22

133

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 10 May 2026 - 12:02

score 101 · Answer 7 · 2026-04-29 12:44:28

101

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Mid-point convexity and convexity

Published on 29 Apr 2026 - 12:44

score 206 · Answer 8 · 2026-05-10 19:57:38

206

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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 10 May 2026 - 19:57

score 133 · Answer 9 · 2026-04-29 12:44:24

133

Views

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

Published on 29 Apr 2026 - 12:44

score 113 · Answer 10 · 2026-04-29 12:44:31

113

Views

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

Published on 29 Apr 2026 - 12:44

score 278 · Answer 11 · 2026-05-06 05:38:31

278

Views

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

Published on 06 May 2026 - 5:38

score 107 · Answer 12 · 2026-05-10 12:34:01

107

Views

Proof of Convexity by Contradiciton

Published on 10 May 2026 - 12:34

score 86 · Answer 13 · 2026-05-07 20:25:31

86

Views

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

Published on 07 May 2026 - 20:25

score 44 · Answer 14 · 2026-05-10 15:22:05

44

Views

Inequality involving Weibull distribution

Published on 10 May 2026 - 15:22

score 130 · Answer 15 · 2026-05-10 15:02:15

130

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 10 May 2026 - 15:02

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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