List questions from convex-optimization

Published on 22 Mar 2026 - 21:03

35

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Is it a concave function of $x$?

Published on 01 Feb 2018 - 5:20

894

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How to prove that $C=\{x: Ax\le 0\}$ has at most one extreme point?

Published on 01 Feb 2018 - 5:53

32

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Known variables as unknowns in non-linear optimization problem

Published on 24 Mar 2026 - 7:12

2k

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How to find extreme points and directions of $\{x:x_1+2x_2\le 4\}$?

Published on 01 Feb 2018 - 7:59

255

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Sum of strictly positive increasing function and negative decreasing function

Published on 24 Mar 2026 - 13:28

113

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Is it a decreasing function of $x$?

Published on 02 Feb 2018 - 2:34

65

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Justify: since $\nabla f(\cdot)$ is continuous, therefore $\int\limits_0^1 (\nabla^2 f(x+ tp) - \nabla^2 f(x))pdt = o(\|p\|)$

Published on 02 Feb 2018 - 7:47

125

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How to determinate that a constrained inequality system is not empty?

Published on 20 Mar 2026 - 0:51

307

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Show that $d$ is direction of closed convex set.

Published on 03 Feb 2018 - 4:27

382

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Linear Matrix Least Squares with Linear Equality Constraint - Minimize $ {\left\| A - B \right\|}_{F}^{2} $ Subject to $ B x = v $

Published on 23 Mar 2026 - 15:04

2.1k

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Extreme directions of $S=\{x:-x_1+2x_2\le 4,x_1-3x_2\le 3,x_1,x_2\ge 0\}$

Published on 03 Feb 2018 - 22:05

162

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Where do these problems fall in the "convex problem class" hierarchy?

Published on 04 Feb 2018 - 7:23

141

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Is $\frac{1}{xy}\log(xya+1)$ a convex function over the domain $x, y \in (0,1], a>0$

Published on 04 Feb 2018 - 17:24

113

Views

$ f(-f(x)) = -x , f(0) = 0$

Published on 24 Mar 2026 - 19:01

List Question

Are these theorems equivalent (notation variation)?

Is it a concave function of $x$?

How to prove that $C=\{x: Ax\le 0\}$ has at most one extreme point?

Known variables as unknowns in non-linear optimization problem

How to find extreme points and directions of $\{x:x_1+2x_2\le 4\}$?

Sum of strictly positive increasing function and negative decreasing function

Is it a decreasing function of $x$?

Justify: since $\nabla f(\cdot)$ is continuous, therefore $\int\limits_0^1 (\nabla^2 f(x+ tp) - \nabla^2 f(x))pdt = o(\|p\|)$

How to determinate that a constrained inequality system is not empty?

Show that $d$ is direction of closed convex set.

Linear Matrix Least Squares with Linear Equality Constraint - Minimize $ {\left\| A - B \right\|}_{F}^{2} $ Subject to $ B x = v $

Extreme directions of $S=\{x:-x_1+2x_2\le 4,x_1-3x_2\le 3,x_1,x_2\ge 0\}$

Where do these problems fall in the "convex problem class" hierarchy?

Is $\frac{1}{xy}\log(xya+1)$ a convex function over the domain $x, y \in (0,1], a>0$

$ f(-f(x)) = -x , f(0) = 0$

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