Question

$\max_{i\in \{1,...,M\}} (a_i+ r_i)$ strictly convex?

score 215 · Answer 1 · 2018-05-25 11:40:15

215

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$\max_{i\in \{1,...,M\}} (a_i+ r_i)$ strictly convex?

Published on 25 May 2018 - 11:40

score 4.7k · Answer 2 · 2018-05-25 13:16:40

4.7k

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Integral of a convex function is convex?

Published on 25 May 2018 - 13:16

score 174 · Answer 3 · 2018-05-25 18:44:45

174

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Show $\max_{r\equiv (r_1,..., r_M) \in \mathbb{R}^M} \sum_{k=1}^M \mu_k r_k - \log\Big(\sum_{k=1}^M \exp(r_k) \Big)= \sum_{k=1}^M \mu_k \log(\mu_k)$

Published on 25 May 2018 - 18:44

score 112 · Answer 4 · 2026-03-25 21:49:39

112

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Infimum of $\max(0,y) + \frac{1}{2t}(x-y)^2$

Published on 25 Mar 2026 - 21:49

score 88 · Answer 5 · 2018-05-27 15:29:33

88

Views

Minimum value of $\frac{x^2+y^2}{x+y}+\frac{y^2+z^2}{y+z}+\frac{z^2+x^2}{z+x}$

Published on 27 May 2018 - 15:29

score 98 · Answer 6 · 2026-03-22 19:34:33

98

Views

Seeking the Maximum of a Product expression using Inequalities

Published on 22 Mar 2026 - 19:34

score 566 · Answer 7 · 2018-05-28 16:58:46

566

Views

Finding Maxima/Minima of Trig Functions (Calculus)

Published on 28 May 2018 - 16:58

score 79 · Answer 8 · 2018-05-28 19:27:12

79

Views

Showing $f(x,y):=(y^2-x^2)(y^2-2x^2)$ has no extrema

Published on 28 May 2018 - 19:27

score 28 · Answer 9 · 2018-05-29 03:20:04

28

Views

Analyze the existence of extremes given a square and a scalar field $f$

Published on 29 May 2018 - 3:20

score 303 · Answer 10 · 2018-05-29 04:34:55

303

Views

Given a Taylor polynomial of degree $2$, study if there is a saddle point at a point

Published on 29 May 2018 - 4:34

score 394 · Answer 11 · 2026-03-22 21:23:42

394

Views

Rearrangement inequality and minimal value of $\frac{\sin^3x}{\cos x} +\frac{\cos^3x}{\sin x}$

Published on 22 Mar 2026 - 21:23

score 138 · Answer 12 · 2026-03-25 07:45:56

138

Views

$a_1 + a_2 + a_3 + a_4 + a_5=0$ and $\displaystyle\max_{1\le i<j\le 5} |a_i - a_j|\le1 \implies a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 \le 10$.

Published on 25 Mar 2026 - 7:45

score 35 · Answer 13 · 2018-05-31 14:41:07

35

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Prove that $\max(n,\min(k,q))=\min(\max(n,k),\max(n,q))$.

Published on 31 May 2018 - 14:41

score 44 · Answer 14 · 2018-05-31 15:01:09

44

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The minimum of the function is only taken on in the $(\sqrt{2\pi}c_{-N},...,\sqrt{2\pi}c_{N})$ where $c_{k}$ are fourier coefficients

Published on 31 May 2018 - 15:01

score 110 · Answer 15 · 2026-03-25 04:35:23

110

Views

Finding bounded extrema of a function

Published on 25 Mar 2026 - 4:35

List Question

$\max_{i\in \{1,...,M\}} (a_i+ r_i)$ strictly convex?

Integral of a convex function is convex?

Show $\max_{r\equiv (r_1,..., r_M) \in \mathbb{R}^M} \sum_{k=1}^M \mu_k r_k - \log\Big(\sum_{k=1}^M \exp(r_k) \Big)= \sum_{k=1}^M \mu_k \log(\mu_k)$

Infimum of $\max(0,y) + \frac{1}{2t}(x-y)^2$

Minimum value of $\frac{x^2+y^2}{x+y}+\frac{y^2+z^2}{y+z}+\frac{z^2+x^2}{z+x}$

Seeking the Maximum of a Product expression using Inequalities

Finding Maxima/Minima of Trig Functions (Calculus)

Showing $f(x,y):=(y^2-x^2)(y^2-2x^2)$ has no extrema

Analyze the existence of extremes given a square and a scalar field $f$

Given a Taylor polynomial of degree $2$, study if there is a saddle point at a point

Rearrangement inequality and minimal value of $\frac{\sin^3x}{\cos x} +\frac{\cos^3x}{\sin x}$

$a_1 + a_2 + a_3 + a_4 + a_5=0$ and $\displaystyle\max_{1\le i<j\le 5} |a_i - a_j|\le1 \implies a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 \le 10$.

Prove that $\max(n,\min(k,q))=\min(\max(n,k),\max(n,q))$.

The minimum of the function is only taken on in the $(\sqrt{2\pi}c_{-N},...,\sqrt{2\pi}c_{N})$ where $c_{k}$ are fourier coefficients

Finding bounded extrema of a function

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