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How to verify Slater's conditions for a convex optimisation problem under box constraints?

score 277 · Answer 1 · 2026-03-26 12:47:00

277

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How to verify Slater's conditions for a convex optimisation problem under box constraints?

Published on 26 Mar 2026 - 12:47

score 47 · Answer 2 · 2026-04-03 06:30:46

47

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Optimization with variable being a set

Published on 03 Apr 2026 - 6:30

score 164 · Answer 3 · 2020-06-05 22:52:43

164

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Let $x^\star =\arg \min_{x \in C} f(x)$. Is it true that $\langle x-x^\star, \nabla f(x^\star) \rangle \ge 0$?

Published on 05 Jun 2020 - 22:52

score 303 · Answer 4 · 2026-03-26 12:16:54

303

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Dual of Lagrange Dual

Published on 26 Mar 2026 - 12:16

score 442 · Answer 5 · 2026-03-27 07:17:03

442

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Convex formulation of the smallest distance to a point outside of a polyhedron

Published on 27 Mar 2026 - 7:17

score 156 · Answer 6 · 2026-03-28 11:03:48

156

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Resolvent of maximal-monotone operator

Published on 28 Mar 2026 - 11:03

score 292 · Answer 7 · 2020-06-06 17:14:18

292

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Stochastic gradient descent for a function of multiple variables?

Published on 06 Jun 2020 - 17:14

score 66 · Answer 8 · 2026-03-30 14:11:18

66

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Find $\frac{{dy(0)}}{{dx}}$ for $x \ge 0$, where, $y = Q(\sqrt x )$?

Published on 30 Mar 2026 - 14:11

score 42 · Answer 9 · 2026-03-27 19:31:57

42

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Can convex function contains fraction term? I have one specific function. Can someone help me clarify whether it is a convex function or not?

Published on 27 Mar 2026 - 19:31

score 146 · Answer 10 · 2026-03-29 04:34:15

146

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Is the relative interior stable under intersection

Published on 29 Mar 2026 - 4:34

score 90 · Answer 11 · 2020-06-07 12:13:52

90

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Where can I find this paper by Bonsall? (Quaterly Journal of Mathematics, 1991) (atomic decomposition, Minkowski functional)

Published on 07 Jun 2020 - 12:13

score 171 · Answer 12 · 2020-06-07 20:15:06

171

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Form Dirichlet Log Density with DCP ruleset.

Published on 07 Jun 2020 - 20:15

score 2k · Answer 13 · 2026-03-29 13:21:36

2k

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How is the subgradient method different from gradient descent in practice?

Published on 29 Mar 2026 - 13:21

score 425 · Answer 14 · 2026-04-02 08:53:34

425

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Minimizing a composite non-differentiable convex function over a $2$-norm ball

Published on 02 Apr 2026 - 8:53

score 418 · Answer 15 · 2026-04-01 11:18:01

418

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Show that the weighted average of a vector is convex when the weights are provided by the softmax function

Published on 01 Apr 2026 - 11:18

List Question

How to verify Slater's conditions for a convex optimisation problem under box constraints?

Optimization with variable being a set

Let $x^\star =\arg \min_{x \in C} f(x)$. Is it true that $\langle x-x^\star, \nabla f(x^\star) \rangle \ge 0$?

Dual of Lagrange Dual

Convex formulation of the smallest distance to a point outside of a polyhedron

Resolvent of maximal-monotone operator

Stochastic gradient descent for a function of multiple variables?

Find $\frac{{dy(0)}}{{dx}}$ for $x \ge 0$, where, $y = Q(\sqrt x )$?

Can convex function contains fraction term? I have one specific function. Can someone help me clarify whether it is a convex function or not?

Is the relative interior stable under intersection

Where can I find this paper by Bonsall? (Quaterly Journal of Mathematics, 1991) (atomic decomposition, Minkowski functional)

Form Dirichlet Log Density with DCP ruleset.

How is the subgradient method different from gradient descent in practice?

Minimizing a composite non-differentiable convex function over a $2$-norm ball

Show that the weighted average of a vector is convex when the weights are provided by the softmax function

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