Question

Does local convexity imply global convexity around a minimum?

score 93 · Answer 1 · 2026-03-25 12:49:01

93

Views

Does local convexity imply global convexity around a minimum?

Published on 25 Mar 2026 - 12:49

score 143 · Answer 2 · 2026-03-25 12:46:16

143

Views

Does this bound hold beyond the domain where the function is convex?

Published on 25 Mar 2026 - 12:46

score 149 · Answer 3 · 2026-03-25 14:25:51

149

Views

Prove that $\Gamma(\operatorname{W}(x))$ is convex $\forall x>0$

Published on 25 Mar 2026 - 14:25

score 63 · Answer 4 · 2026-03-25 12:49:47

63

Views

Prove the inequality $\frac{1}{1+a+b}+\frac{1}{1+c+b}+\frac{1}{1+a+c}+a+b+c \le 3 + \frac 13 (ab+bc+ac)$

Published on 25 Mar 2026 - 12:49

score 340 · Answer 5 · 2026-03-25 12:49:56

340

Views

Find the minimum value of $\sqrt{x+y}+\sqrt{(1-x)+y}+\sqrt{x+(1-y)}+\sqrt{(1-x)+(1-y)}$

Published on 25 Mar 2026 - 12:49

score 982 · Answer 6 · 2026-03-25 12:50:53

982

Views

find the maximum $\frac{\frac{x^2_{1}}{x_{2}}+\frac{x^2_{2}}{x_{3}}+\cdots+\frac{x^2_{n-1}}{x_{n}}+\frac{x^2_{n}}{x_{1}}}{x_{1}+x_{2}+\cdots+x_{n}}$

Published on 25 Mar 2026 - 12:50

score 92 · Answer 7 · 2026-03-25 19:06:58

92

Views

How can I show that $\left|\sin \frac{s}{2}\right| \geq \frac{|s|}{\pi}, s \in [- \pi , \pi]$?

Published on 25 Mar 2026 - 19:06

score 374 · Answer 8 · 2026-03-25 16:03:48

374

Views

Inequality for positive real numbers less than $1$: $8(abcd+1)>(a+1)(b+1)(c+1)(d+1)$

Published on 25 Mar 2026 - 16:03

score 139 · Answer 9 · 2026-03-25 14:24:34

139

Views

Proving that $2\left(a+b\right)\ln{\left(\frac{a+b}{2}\right)}\geq\left(a+1\right)\ln{\left(a\right)}+\left(b+1\right)\ln{\left(b\right)}$

Published on 25 Mar 2026 - 14:24

score 169 · Answer 10 · 2026-03-25 12:54:41

169

Views

Does the $\log$-$\exp$ analogous of Minkowski integral inequality hold true?

Published on 25 Mar 2026 - 12:54

score 38 · Answer 11 · 2026-03-25 12:55:00

38

Views

Can we rewrite a nonlinear constraint as a multiplication of real and integer as convex?

Published on 25 Mar 2026 - 12:55

score 47 · Answer 12 · 2026-03-25 12:53:06

47

Views

A question on a derivation from Hajek's book.

Published on 25 Mar 2026 - 12:53

score 71 · Answer 13 · 2026-04-28 15:17:21

71

Views

Difference between majorization and weak majorization.

Published on 28 Apr 2026 - 15:17

score 75 · Answer 14 · 2026-03-25 12:54:25

75

Views

How to prove $\left(\frac{e^n-1}{n}\right)^{2n+1} \leq \frac{(e-1)(e^2-1)...(e^{2n}-1)}{(2n)!}$?

Published on 25 Mar 2026 - 12:54

score 106 · Answer 15 · 2026-03-25 07:43:53

106

Views

Prove by using convexity: $33\sin33^{\circ}+29\sin29^{\circ}+28\sin28^{\circ}>45$

Published on 25 Mar 2026 - 7:43

List Question

Does local convexity imply global convexity around a minimum?

Does this bound hold beyond the domain where the function is convex?

Prove that $\Gamma(\operatorname{W}(x))$ is convex $\forall x>0$

Prove the inequality $\frac{1}{1+a+b}+\frac{1}{1+c+b}+\frac{1}{1+a+c}+a+b+c \le 3 + \frac 13 (ab+bc+ac)$

Find the minimum value of $\sqrt{x+y}+\sqrt{(1-x)+y}+\sqrt{x+(1-y)}+\sqrt{(1-x)+(1-y)}$

find the maximum $\frac{\frac{x^2_{1}}{x_{2}}+\frac{x^2_{2}}{x_{3}}+\cdots+\frac{x^2_{n-1}}{x_{n}}+\frac{x^2_{n}}{x_{1}}}{x_{1}+x_{2}+\cdots+x_{n}}$

How can I show that $\left|\sin \frac{s}{2}\right| \geq \frac{|s|}{\pi}, s \in [- \pi , \pi]$?

Inequality for positive real numbers less than $1$: $8(abcd+1)>(a+1)(b+1)(c+1)(d+1)$

Proving that $2\left(a+b\right)\ln{\left(\frac{a+b}{2}\right)}\geq\left(a+1\right)\ln{\left(a\right)}+\left(b+1\right)\ln{\left(b\right)}$

Does the $\log$-$\exp$ analogous of Minkowski integral inequality hold true?

Can we rewrite a nonlinear constraint as a multiplication of real and integer as convex?

A question on a derivation from Hajek's book.

Difference between majorization and weak majorization.

How to prove $\left(\frac{e^n-1}{n}\right)^{2n+1} \leq \frac{(e-1)(e^2-1)...(e^{2n}-1)}{(2n)!}$?

Prove by using convexity: $33\sin33^{\circ}+29\sin29^{\circ}+28\sin28^{\circ}>45$

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