List questions from convex-analysis

Published on 10 May 2026 - 15:09

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Prove that $f (y) \geq f(x) + f'(x)(y-x)$ for all $x, y \in (a,b)$.

Published on 16 Apr 2026 - 14:31

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Show that if $f_1, \dots, f_m: \mathbb{R}^n \to \mathbb{R}$ are piecewise linear convex, then $\sum_{i=1}^{m}f_i$ is piecewise linear convex as well.

Published on 16 Apr 2026 - 10:22

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Show that the Huber-loss based optimization is equivalent to $\ell_1$ norm based.

Published on 11 May 2026 - 5:03

379

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Convex function and inequality (slope)

Published on 13 Apr 2026 - 8:34

122

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Connectivity and Inverse Function Theorem.

Published on 11 Apr 2026 - 6:56

548

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Matrix fractional function

Published on 11 Apr 2026 - 17:06

96

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Why am I getting exactly same expression for the affine underestimator?

Published on 16 Apr 2026 - 10:09

334

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Maximization of bilinear objective over convex body

Published on 11 May 2026 - 3:06

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Convexity of a convex set minus points close to its frontier.

Published on 10 May 2026 - 20:17

477

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Are the following polynomials convex (or concave) on the interval $[0,1]^3$?

Published on 16 Apr 2026 - 8:31

83

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Concavity of a simple objective function

Published on 11 May 2026 - 1:55

63

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Defining conic problems over some specific cone

Published on 10 May 2026 - 14:03

70

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Under what conditions the globally optimal solution and solution obtained by step-by-step optimization are the same?

Published on 12 Apr 2026 - 16:51

347

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Boyd & Vandenberghe, example 3.4 — question on Schur complements and LMIs

Published on 11 May 2026 - 3:33

List Question

Orthogonal Projection onto $ {L}_{1} $ Ball with Box Constraints

Prove that $f (y) \geq f(x) + f'(x)(y-x)$ for all $x, y \in (a,b)$.

Show that if $f_1, \dots, f_m: \mathbb{R}^n \to \mathbb{R}$ are piecewise linear convex, then $\sum_{i=1}^{m}f_i$ is piecewise linear convex as well.

Show that the Huber-loss based optimization is equivalent to $\ell_1$ norm based.

Convex function and inequality (slope)

Connectivity and Inverse Function Theorem.

Matrix fractional function

Why am I getting exactly same expression for the affine underestimator?

Maximization of bilinear objective over convex body

Convexity of a convex set minus points close to its frontier.

Are the following polynomials convex (or concave) on the interval $[0,1]^3$?

Concavity of a simple objective function

Defining conic problems over some specific cone

Under what conditions the globally optimal solution and solution obtained by step-by-step optimization are the same?

Boyd & Vandenberghe, example 3.4 — question on Schur complements and LMIs

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