List questions from convex-analysis

Published on 26 Nov 2018 - 15:32

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Convex function's monotonicity?

Published on 27 Nov 2018 - 12:32

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How to prove a matrix function is convex or nonconvex?

Published on 26 Mar 2026 - 9:38

197

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Second order necessary and sufficient conditions for convex nonsmooth optimization

Published on 30 Mar 2026 - 10:52

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Newton-Raphson on strictly convex function

Published on 25 Mar 2026 - 7:47

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Convexity of a Function Implies Function Lies Above Any Tangent Line

Published on 29 Nov 2018 - 22:39

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why when $X=qq^T \in S^n_+$,then $tr(XY) \lt 0$,it means that $Y \notin \mathbf K^*$?

Published on 25 Mar 2026 - 4:43

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For a convex function $f$, is the following set convex: $X := \{x ∶ -f(x) \leq 1 \}$?

Published on 26 Mar 2026 - 13:30

268

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Prove that $\Vert\cdot \Vert^2:X\to \Bbb{R},$ where $X$ is a vector space, is convex

Published on 31 Mar 2026 - 16:14

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why can we use this $x^\theta y^{1-\theta} \le \theta x+(1-\theta)y$ to prove the $\prod \limits_{i=1}^{n}x_i \ge 1$ is convex set?

Published on 29 Mar 2026 - 10:59

112

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Prove that set is convex.

Published on 29 Mar 2026 - 9:09

263

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Do $|f'|$ and $f$ have the same minimisers for strictly convex functions?

Published on 25 Mar 2026 - 22:03

346

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Is minimizing the norm of a vector equivalent to minimizing the square of the norm?

Published on 29 Mar 2026 - 5:43

72

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Prove point is in closure of set

Published on 29 Mar 2026 - 11:02

162

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Connection/Consistency Between Different Definitions of Polyhedron? And How Does This Proof Apply to This Definition?

Published on 25 Mar 2026 - 20:13

List Question

Defintion of strictly concave

Convex function's monotonicity?

How to prove a matrix function is convex or nonconvex?

Second order necessary and sufficient conditions for convex nonsmooth optimization

Newton-Raphson on strictly convex function

Convexity of a Function Implies Function Lies Above Any Tangent Line

why when $X=qq^T \in S^n_+$,then $tr(XY) \lt 0$,it means that $Y \notin \mathbf K^*$?

For a convex function $f$, is the following set convex: $X := \{x ∶ -f(x) \leq 1 \}$?

Prove that $\Vert\cdot \Vert^2:X\to \Bbb{R},$ where $X$ is a vector space, is convex

why can we use this $x^\theta y^{1-\theta} \le \theta x+(1-\theta)y$ to prove the $\prod \limits_{i=1}^{n}x_i \ge 1$ is convex set?

Prove that set is convex.

Do $|f'|$ and $f$ have the same minimisers for strictly convex functions?

Is minimizing the norm of a vector equivalent to minimizing the square of the norm?

Prove point is in closure of set

Connection/Consistency Between Different Definitions of Polyhedron? And How Does This Proof Apply to This Definition?

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