List questions from convex-optimization

Published on 11 Apr 2026 - 12:17

26

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Prove that $C = \{(x_1,x_2,0)\in R^3 | x_1^2+x_2^2 \leq 1\}$ is closed, dim(C)=2 and find ri(C)

Published on 16 Apr 2026 - 12:11

110

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The slope and intercept of piecewise linear functions

Published on 12 Apr 2026 - 10:17

276

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Convex hull of idempotent matrices

Published on 14 Apr 2026 - 18:15

387

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Let C be a nonempty, closed convex subset of X. Let $x,y\in X$. Show that $y=P_c(x)\iff y\in (Id + N_c)^{-1}(x)$.

Published on 11 Oct 2015 - 4:00

3.5k

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Subderivative of $ ||Au||_{L^{\infty}} $ to Compute Proximal Operator / Prox Operator

Published on 18 Apr 2026 - 20:47

74

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Consider the Hilbert product space $X\times X$

Published on 21 Apr 2026 - 17:22

4.4k

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Legendre transform of a norm

Published on 20 Apr 2026 - 9:23

462

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Projection of a hyperplane

Published on 11 Apr 2026 - 14:37

166

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A complex optimization problem (maximize determinant of matrix)

Published on 20 Apr 2026 - 12:17

1.4k

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The Proximal Operator of a Function with $ {L}_{1} $ Norm and Affine Term

Published on 15 Oct 2015 - 6:14

74

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Optimization function convex or not

Published on 06 Apr 2026 - 14:21

382

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Under what conditions does a convex objective function have a concave value function?

Published on 20 Apr 2026 - 12:19

114

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Holding the constraints of a constrained optimization when transformed into unconstrained optimization

Published on 17 Apr 2026 - 0:57

56

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is the Superellipse function convex or not?

Published on 23 Apr 2026 - 2:34

List Question

how do i show that a function $f(x)$ is convex given that the inequality holds

Prove that $C = \{(x_1,x_2,0)\in R^3 | x_1^2+x_2^2 \leq 1\}$ is closed, dim(C)=2 and find ri(C)

The slope and intercept of piecewise linear functions

Convex hull of idempotent matrices

Let C be a nonempty, closed convex subset of X. Let $x,y\in X$. Show that $y=P_c(x)\iff y\in (Id + N_c)^{-1}(x)$.

Subderivative of $ ||Au||_{L^{\infty}} $ to Compute Proximal Operator / Prox Operator

Consider the Hilbert product space $X\times X$

Legendre transform of a norm

Projection of a hyperplane

A complex optimization problem (maximize determinant of matrix)

The Proximal Operator of a Function with $ {L}_{1} $ Norm and Affine Term

Optimization function convex or not

Under what conditions does a convex objective function have a concave value function?

Holding the constraints of a constrained optimization when transformed into unconstrained optimization

is the Superellipse function convex or not?

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