Question

The Proximal Operator of the $ {L}_{1} $ Norm Function

score 19.5k · Answer 1 · 2026-04-10 20:42:45

19.5k

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The Proximal Operator of the $ {L}_{1} $ Norm Function

Published on 10 Apr 2026 - 20:42

score 39 · Answer 2 · 2026-04-11 06:36:19

39

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Some questions about convexity, compact sets

Published on 11 Apr 2026 - 6:36

score 800 · Answer 3 · 2026-04-14 23:54:25

800

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What is the convex conjugate (fenchel conjugate) of $f(x)=\lambda \|x\|_1$?

Published on 14 Apr 2026 - 23:54

score 219 · Answer 4 · 2026-04-16 18:56:30

219

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Proximal Operator for $ f \left( \boldsymbol{x} \right) = - \log \left(x_1 \cdot x_2 \cdot \ldots \cdot x_n \right) $

Published on 16 Apr 2026 - 18:56

score 508 · Answer 5 · 2026-04-10 13:36:23

508

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How to derive the dual for min-cut problem?

Published on 10 Apr 2026 - 13:36

score 198 · Answer 6 · 2026-04-11 21:04:23

198

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The dual of a circular cone

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score 124 · Answer 7 · 2026-04-15 03:54:44

124

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Identifying whether a set, such as $V = \{ x \in \mathbb{R^5}: 2x_1 - x_4 < 7 \}$, is convex/open/closed/bounded/compact

Published on 15 Apr 2026 - 3:54

score 60 · Answer 8 · 2026-04-16 09:08:59

60

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Upper bound of a specific function: $ \left(\frac{\sqrt{2}-1}{\sqrt{2}-2^{\tiny\frac{2p-1}{2p}}}\right)^p$

Published on 16 Apr 2026 - 9:08

score 240 · Answer 9 · 2026-04-09 20:09:06

240

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Can we use KKT condition to derive the dual of an optimization function given that Slater's condition holds?

Published on 09 Apr 2026 - 20:09

score 102 · Answer 10 · 2026-04-15 09:55:45

102

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A star domain $S$ such that $S \cap B(x,r)$ is not a star domain

Published on 15 Apr 2026 - 9:55

score 100 · Answer 11 · 2026-04-15 19:50:09

100

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Prove $f(x)=(x-3)^2 +4$ is a convex function

Published on 15 Apr 2026 - 19:50

score 101 · Answer 12 · 2026-04-13 12:07:11

101

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Published on 13 Apr 2026 - 12:07

score 724 · Answer 13 · 2026-04-14 04:27:42

724

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Every closed convex cone in $ \mathbb{R}^2 $ is polyhedral

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score 617 · Answer 14 · 2026-04-11 23:47:46

617

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How to derive the general form of Moreau Decomposition?

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score 458 · Answer 15 · 2026-04-11 18:56:55

458

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Proving a set is convex

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List Question

The Proximal Operator of the $ {L}_{1} $ Norm Function

Some questions about convexity, compact sets

What is the convex conjugate (fenchel conjugate) of $f(x)=\lambda \|x\|_1$?

Proximal Operator for $ f \left( \boldsymbol{x} \right) = - \log \left(x_1 \cdot x_2 \cdot \ldots \cdot x_n \right) $

How to derive the dual for min-cut problem?

The dual of a circular cone

Identifying whether a set, such as $V = \{ x \in \mathbb{R^5}: 2x_1 - x_4 < 7 \}$, is convex/open/closed/bounded/compact

Upper bound of a specific function: $ \left(\frac{\sqrt{2}-1}{\sqrt{2}-2^{\tiny\frac{2p-1}{2p}}}\right)^p$

Can we use KKT condition to derive the dual of an optimization function given that Slater's condition holds?

A star domain $S$ such that $S \cap B(x,r)$ is not a star domain

Prove $f(x)=(x-3)^2 +4$ is a convex function

$C \subset V$ convex $\Rightarrow$ $C$ locally connected

Every closed convex cone in $ \mathbb{R}^2 $ is polyhedral

How to derive the general form of Moreau Decomposition?

Proving a set is convex

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