Question

Show that the function is convex

score 212 · Answer 1 · 2019-02-15 10:39:22

212

Views

Show that the function is convex

Published on 15 Feb 2019 - 10:39

score 898 · Answer 2 · 2019-02-16 11:21:20

898

Views

Proof (without use of differential calculus) that $e^{\sqrt{x}}$ is convex on $[1,+\infty)$.

Published on 16 Feb 2019 - 11:21

score 343 · Answer 3 · 2019-02-16 12:03:49

343

Views

If $f$ is convex and concave on interval $I$, then $f$ is affine on $I$

Published on 16 Feb 2019 - 12:03

score 512 · Answer 4 · 2019-02-16 18:02:29

512

Views

Without use of derivatives, prove that function $(1+x^p)^{1/p}$ is convex for $p\geq 1$

Published on 16 Feb 2019 - 18:02

score 64 · Answer 5 · 2026-03-25 04:34:54

64

Views

Variable selection in mixed linear integer programming or mixed integer programming with convex constraints and objective

Published on 25 Mar 2026 - 4:34

score 44 · Answer 6 · 2019-02-17 00:08:28

44

Views

When does a convex sequence $S_n$ satisfy $S_{a+b+c} - (S_{a+b}+S_{a+c}+S_{b+c})+S_a+S_b+S_c\geq 0$

Published on 17 Feb 2019 - 0:08

score 43 · Answer 7 · 2026-03-30 05:25:23

43

Views

Proof $C$= {$(x, y) \in \mathbb{R}^2 | x+y=b $} is convex

Published on 30 Mar 2026 - 5:25

score 60 · Answer 8 · 2019-02-17 15:49:57

60

Views

Continuous $f:(a,b)\to \mathbb{R}$ is convex iff $x \mapsto f(x)+\gamma x+\delta$ does not attain max for all $\gamma,~\delta\in \mathbb{R}$

Published on 17 Feb 2019 - 15:49

score 133 · Answer 9 · 2026-03-26 11:16:15

133

Views

Inequality constraints and the max function

Published on 26 Mar 2026 - 11:16

score 63 · Answer 10 · 2019-02-18 11:07:54

63

Views

Using Jensen's inequality prove: (1) $~n!<n^n<(n!)^2$ for $n>1$ and (2) $~e^n\geqslant \frac{n^n}{n!}.$

Published on 18 Feb 2019 - 11:07

score 92 · Answer 11 · 2026-03-26 00:53:40

92

Views

What is the gradient of $\operatorname{trace}(XCP(XC)^T)$?

Published on 26 Mar 2026 - 0:53

score 124 · Answer 12 · 2026-03-26 03:01:43

124

Views

Proof that makes use of the differentiability of a function and of its convex conjugate

Published on 26 Mar 2026 - 3:01

score 113 · Answer 13 · 2019-02-19 08:08:11

113

Views

Convexity of a set function

Published on 19 Feb 2019 - 8:08

score 146 · Answer 14 · 2019-02-19 16:38:46

146

Views

If $‎{\lim_{n\to\infty}}(f(n) - f(n+1)) = 0‎$, then $‎{\lim_{x\to\infty}}f(x) = L‎$.

Published on 19 Feb 2019 - 16:38

score 381 · Answer 15 · 2026-03-28 13:35:05

381

Views

Does increasing differences imply convexity of a function?

Published on 28 Mar 2026 - 13:35

List Question

Show that the function is convex

Proof (without use of differential calculus) that $e^{\sqrt{x}}$ is convex on $[1,+\infty)$.

If $f$ is convex and concave on interval $I$, then $f$ is affine on $I$

Without use of derivatives, prove that function $(1+x^p)^{1/p}$ is convex for $p\geq 1$

Variable selection in mixed linear integer programming or mixed integer programming with convex constraints and objective

When does a convex sequence $S_n$ satisfy $S_{a+b+c} - (S_{a+b}+S_{a+c}+S_{b+c})+S_a+S_b+S_c\geq 0$

Proof $C$= {$(x, y) \in \mathbb{R}^2 | x+y=b $} is convex

Continuous $f:(a,b)\to \mathbb{R}$ is convex iff $x \mapsto f(x)+\gamma x+\delta$ does not attain max for all $\gamma,~\delta\in \mathbb{R}$

Inequality constraints and the max function

Using Jensen's inequality prove: (1) $~n!<n^n<(n!)^2$ for $n>1$ and (2) $~e^n\geqslant \frac{n^n}{n!}.$

What is the gradient of $\operatorname{trace}(XCP(XC)^T)$?

Proof that makes use of the differentiability of a function and of its convex conjugate

Convexity of a set function

If $‎{\lim_{n\to\infty}}(f(n) - f(n+1)) = 0‎$, then $‎{\lim_{x\to\infty}}f(x) = L‎$.

Does increasing differences imply convexity of a function?

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