List questions from convex-analysis

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Are all convex sets Borel sets?

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Determine whether the following sets are convex or not, and explain your reasoning

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Relationship between convex functions and coercivity

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Is $d^2(x,C)$ a convex function?

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The perturbation of convex function can also be convex?

Published on 30 Mar 2026 - 9:49

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Show that the support of a solution of $Ax=b$ is closed and convex

Published on 29 Oct 2018 - 16:12

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Characterization of convex dual-like functions

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closed convex hull of $\{e_n:n\in \mathbb N\}$ in $\ell^1$

Published on 31 Oct 2018 - 2:19

80

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Matrix calculus : Derivative with respect to two vectors

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Separability of Constrained Optimization

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$\min x^TWx$ s.t. $||x||_{\infty} \leq 1, ||x||_2 \leq 1$

Published on 28 Mar 2026 - 19:30

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What is the support function of a convex set in $\mathbb{C}$?

Published on 01 Nov 2018 - 3:02

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If a function is quasiconcave on a curve, does it also have to be quasiconcave on a convex set?

Published on 01 Nov 2018 - 3:17

626

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Orthogonal projection on nuclear-norm ball

Published on 25 Mar 2026 - 8:03

List Question

A natural concave function

Are all convex sets Borel sets?

Determine whether the following sets are convex or not, and explain your reasoning

Relationship between convex functions and coercivity

Is $d^2(x,C)$ a convex function?

The perturbation of convex function can also be convex?

Show that the support of a solution of $Ax=b$ is closed and convex

Characterization of convex dual-like functions

closed convex hull of $\{e_n:n\in \mathbb N\}$ in $\ell^1$

Matrix calculus : Derivative with respect to two vectors

Separability of Constrained Optimization

$\min x^TWx$ s.t. $||x||_{\infty} \leq 1, ||x||_2 \leq 1$

What is the support function of a convex set in $\mathbb{C}$?

If a function is quasiconcave on a curve, does it also have to be quasiconcave on a convex set?

Orthogonal projection on nuclear-norm ball

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