List questions from convex-optimization

Published on 24 Apr 2026 - 17:53

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Let $f:X\rightarrow ]-\infty,+\infty]$, let $b\in x$ and let $c\in X$. Find Fenchel conjugates of the functions:

Published on 16 Nov 2015 - 20:08

3.3k

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Euclidean Projection onto the $ {L}_{2, 1} $ Norm

Published on 29 Mar 2026 - 12:07

133

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Regression maximum likelihood

Published on 02 Apr 2026 - 0:56

327

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High-dimensional optimization issue

Published on 31 Mar 2026 - 6:03

68

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A nonlinear optimization problem with difficult Kuhn-Tucker system of equations

Published on 07 Apr 2026 - 5:02

338

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Nuclear norm regularization of symmetric matrix

Published on 17 Apr 2026 - 20:53

1.4k

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How to extract the positive semidefinite part of a matrix

Published on 20 Nov 2015 - 2:55

144

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Prove that a function is convex by only using positive semi-definiteness

Published on 20 Nov 2015 - 8:58

168

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Equivalent formulation of linear discrimination problem on Boyd convex optimization slides

Published on 04 Apr 2026 - 10:22

3.4k

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Prove that a polytope is closed

Published on 21 Nov 2015 - 0:38

306

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Prove or disprove convexity

Published on 07 Apr 2026 - 5:02

1.7k

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Examples of $f$ strictly convex, either with one minimizer or with no minimizer.

Published on 22 Nov 2015 - 3:07

59

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Given $\min\limits_x \|x\|_2^2 \quad \text{s.t.} \quad Ax = b$ show $x^* = A^T(AA^T)^{-1}b$

Published on 22 Nov 2015 - 5:18

336

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Solution of constrained optimization problem (ADMM)

Published on 05 Apr 2026 - 1:39

List Question

Weighted $L_1$ norm

Let $f:X\rightarrow ]-\infty,+\infty]$, let $b\in x$ and let $c\in X$. Find Fenchel conjugates of the functions:

Euclidean Projection onto the $ {L}_{2, 1} $ Norm

Regression maximum likelihood

High-dimensional optimization issue

A nonlinear optimization problem with difficult Kuhn-Tucker system of equations

Nuclear norm regularization of symmetric matrix

How to extract the positive semidefinite part of a matrix

Prove that a function is convex by only using positive semi-definiteness

Equivalent formulation of linear discrimination problem on Boyd convex optimization slides

Prove that a polytope is closed

Prove or disprove convexity

Examples of $f$ strictly convex, either with one minimizer or with no minimizer.

Given $\min\limits_x \|x\|_2^2 \quad \text{s.t.} \quad Ax = b$ show $x^* = A^T(AA^T)^{-1}b$

Solution of constrained optimization problem (ADMM)

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