Question

Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

score 139 · Answer 1 · 2026-03-26 01:25:16

139

Views

Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

Published on 26 Mar 2026 - 1:25

score 856 · Answer 2 · 2026-03-25 06:21:22

856

Views

Getting the final solution for the subgradient of function $F(x) := \max \{0, \frac1{2}(x^2 - 1)\}$

Published on 25 Mar 2026 - 6:21

score 1.1k · Answer 3 · 2026-03-28 22:28:02

1.1k

Views

Sketch the sets in $\mathbb C$ and determine whether they are open, closed, or neither; bounded; connected and their boundaries.

Published on 28 Mar 2026 - 22:28

score 33 · Answer 4 · 2026-03-25 04:58:45

33

Views

Find a mapping from $R^{n \times n}$ to orthogonal matrices in the unit sphere such that distances do not increase.

Published on 25 Mar 2026 - 4:58

score 118 · Answer 5 · 2026-03-25 12:55:43

118

Views

Is $|abc|+|bcd|+|abd|+|acd|$ a norm on $\mathbb{R}^4$?

Published on 25 Mar 2026 - 12:55

score 87 · Answer 6 · 2026-03-25 07:38:24

87

Views

An optimization problem over a bi-linear function

Published on 25 Mar 2026 - 7:38

score 223 · Answer 7 · 2018-07-31 03:22:54

223

Views

An integral inequality with the Hessian of a convex function defined in the unit disk

Published on 31 Jul 2018 - 3:22

score 46 · Answer 8 · 2026-03-23 01:33:47

46

Views

Utility Maximization on a finite Probability Space. Possible mistakes in a paper?

Published on 23 Mar 2026 - 1:33

score 116 · Answer 9 · 2018-07-31 11:14:22

116

Views

Is $f(e^x)$ log-concave if $f$ is positive decreasing convex function on $[0,a]$?

Published on 31 Jul 2018 - 11:14

score 271 · Answer 10 · 2018-07-31 13:40:04

271

Views

Can we approximate a convex function by twice differentiable convex function?

Published on 31 Jul 2018 - 13:40

score 116 · Answer 11 · 2026-03-28 08:29:31

116

Views

Expected Proportion of Random Variables

Published on 28 Mar 2026 - 8:29

score 297 · Answer 12 · 2026-02-23 01:08:25

297

Views

If $f$ is proper, lsc, and $\frac{f(x) + f(y)}{2} = f^{**}\left(\frac{x + y}{2}\right) \implies x = y$, is $f$ necessarily convex?

Published on 23 Feb 2026 - 1:08

score 395 · Answer 13 · 2026-03-25 09:22:55

395

Views

Local minima and maxima over the simplex

Published on 25 Mar 2026 - 9:22

score 223 · Answer 14 · 2026-03-26 02:46:54

223

Views

Is the exponential of the trace convex?

Published on 26 Mar 2026 - 2:46

score 3.7k · Answer 15 · 2026-03-25 10:51:35

3.7k

Views

Gradient of Moreau Envelope

Published on 25 Mar 2026 - 10:51

List Question

Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

Getting the final solution for the subgradient of function $F(x) := \max \{0, \frac1{2}(x^2 - 1)\}$

Sketch the sets in $\mathbb C$ and determine whether they are open, closed, or neither; bounded; connected and their boundaries.

Find a mapping from $R^{n \times n}$ to orthogonal matrices in the unit sphere such that distances do not increase.

Is $|abc|+|bcd|+|abd|+|acd|$ a norm on $\mathbb{R}^4$?

An optimization problem over a bi-linear function

An integral inequality with the Hessian of a convex function defined in the unit disk

Utility Maximization on a finite Probability Space. Possible mistakes in a paper?

Is $f(e^x)$ log-concave if $f$ is positive decreasing convex function on $[0,a]$?

Can we approximate a convex function by twice differentiable convex function?

Expected Proportion of Random Variables

If $f$ is proper, lsc, and $\frac{f(x) + f(y)}{2} = f^{**}\left(\frac{x + y}{2}\right) \implies x = y$, is $f$ necessarily convex?

Local minima and maxima over the simplex

Is the exponential of the trace convex?

Gradient of Moreau Envelope

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