Question

$\|ta+(1-t)b\|^2=t\|a\|^2+(1-t)\|b\|^2-t(1-t)\|a-b\|^2$, Is that true?

score 93 · Answer 1 · 2026-04-01 00:25:34

93

Views

$\|ta+(1-t)b\|^2=t\|a\|^2+(1-t)\|b\|^2-t(1-t)\|a-b\|^2$, Is that true?

Published on 01 Apr 2026 - 0:25

score 1.7k · Answer 2 · 2018-12-20 10:36:14

1.7k

Views

Can a function be neither convex nor concave everywhere?

Published on 20 Dec 2018 - 10:36

score 488 · Answer 3 · 2018-12-20 13:07:23

488

Views

Equivalent definitions of convexity

Published on 20 Dec 2018 - 13:07

score 216 · Answer 4 · 2026-03-29 14:03:05

216

Views

Proving convexity of $h(y) = \inf_{Ax=y}{f(x)}$ for convex $f(x)$ over $\mathbb{R}^n$, and $A\in\mathbb{R}^{m\times n}$

Published on 29 Mar 2026 - 14:03

score 241 · Answer 5 · 2018-12-21 09:41:50

241

Views

Show that the derivative of a convex function is zero as $\lim_{x \rightarrow\infty}{f(x)}=A$

Published on 21 Dec 2018 - 9:41

score 74 · Answer 6 · 2018-12-21 18:20:29

74

Views

Convexity of $f(v) = E[(\sum_i X_i v_i)^k]$ subj. to $\sum_i v_i^2=1$

Published on 21 Dec 2018 - 18:20

score 1.9k · Answer 7 · 2026-03-29 07:32:16

1.9k

Views

Explaining Defitions of Minkowski functional and Gauge Functional

Published on 29 Mar 2026 - 7:32

score 74 · Answer 8 · 2026-03-26 04:30:35

74

Views

how to tell the monotonicity of an implicit function?

Published on 26 Mar 2026 - 4:30

score 60 · Answer 9 · 2018-12-22 12:37:42

60

Views

Grf $\not=$ Cl(epigraph of f) $\cap$ Cl(subgraph of f) can be concave/convex?

Published on 22 Dec 2018 - 12:37

score 1k · Answer 10 · 2018-12-23 19:44:58

1k

Views

How to prove that every open convex set in $\mathbb{R}^{n}$ is homeomorphic to an open ball?

Published on 23 Dec 2018 - 19:44

score 235 · Answer 11 · 2026-03-29 15:59:38

235

Views

Curvature of projection function onto smooth curve

Published on 29 Mar 2026 - 15:59

score 38 · Answer 12 · 2026-03-25 03:18:55

38

Views

Guarantee strict convexity at a point

Published on 25 Mar 2026 - 3:18

score 106 · Answer 13 · 2018-12-24 15:01:21

106

Views

Why does the second derivative of convex function exist almost everywhere?

Published on 24 Dec 2018 - 15:01

score 48 · Answer 14 · 2018-12-25 08:57:03

48

Views

Question about an inequation described by matrices.

Published on 25 Dec 2018 - 8:57

score 118 · Answer 15 · 2018-12-25 11:26:27

118

Views

"algebraic openness" of the epigraph of a sublinear function

Published on 25 Dec 2018 - 11:26

List Question

$\|ta+(1-t)b\|^2=t\|a\|^2+(1-t)\|b\|^2-t(1-t)\|a-b\|^2$, Is that true?

Can a function be neither convex nor concave everywhere?

Equivalent definitions of convexity

Proving convexity of $h(y) = \inf_{Ax=y}{f(x)}$ for convex $f(x)$ over $\mathbb{R}^n$, and $A\in\mathbb{R}^{m\times n}$

Show that the derivative of a convex function is zero as $\lim_{x \rightarrow\infty}{f(x)}=A$

Convexity of $f(v) = E[(\sum_i X_i v_i)^k]$ subj. to $\sum_i v_i^2=1$

Explaining Defitions of Minkowski functional and Gauge Functional

how to tell the monotonicity of an implicit function?

Grf $\not=$ Cl(epigraph of f) $\cap$ Cl(subgraph of f) can be concave/convex?

How to prove that every open convex set in $\mathbb{R}^{n}$ is homeomorphic to an open ball?

Curvature of projection function onto smooth curve

Guarantee strict convexity at a point

Why does the second derivative of convex function exist almost everywhere?

Question about an inequation described by matrices.

"algebraic openness" of the epigraph of a sublinear function

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