List questions from dual-cone

Published on 29 Apr 2026 - 13:27

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A cone in $\mathbb{R}^n$ containing n linearly independent vectors has a non empty interior

Published on 29 Apr 2026 - 13:27

364

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Characterizing the dual cone of the squares of skew-symmetric matrices

Published on 29 Apr 2026 - 13:27

250

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Given a closed, convex, full-dimensional cone $K$, how do I show that $u\in int(K) \iff u^tx>0 \quad \forall x\in K^*-\{0\}$?

Published on 29 Apr 2026 - 13:27

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For full-dimensional cone $K$, $x\in int(K)$, can you take arb. vector $y$ and for some $t$ small enough have that $x-ty\in int(K)$

Published on 29 Apr 2026 - 13:28

262

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Uniqueness of dual variable for convex optimization problem

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103

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Dual problem to SDP problem

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1.2k

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Dual polyhedron & dual cone

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626

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Why are generalized inequalities defined over proper cone?

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How to find the dual cone?

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73

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What mean T in formula?

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56

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Under what cases of cone $K$ is $x = \text{proj}_K(x) + \text{proj}_{-K^*}(x)$ possible for all $x$?

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201

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The dual of a circular cone

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513

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Proof of closure, convex hull and minimal cone of dual set

Published on 29 Apr 2026 - 13:28

105

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The extremal points of the dual polytopes of vertex transitive polytopes

Published on 29 Apr 2026 - 13:28

List Question

Volume cut off from the sphere by the cone using cylindrical polar coordinates

A cone in $\mathbb{R}^n$ containing n linearly independent vectors has a non empty interior

Characterizing the dual cone of the squares of skew-symmetric matrices

Given a closed, convex, full-dimensional cone $K$, how do I show that $u\in int(K) \iff u^tx>0 \quad \forall x\in K^*-\{0\}$?

For full-dimensional cone $K$, $x\in int(K)$, can you take arb. vector $y$ and for some $t$ small enough have that $x-ty\in int(K)$

Uniqueness of dual variable for convex optimization problem

Dual problem to SDP problem

Dual polyhedron & dual cone

Why are generalized inequalities defined over proper cone?

How to find the dual cone?

What mean T in formula?

Under what cases of cone $K$ is $x = \text{proj}_K(x) + \text{proj}_{-K^*}(x)$ possible for all $x$?

The dual of a circular cone

Proof of closure, convex hull and minimal cone of dual set

The extremal points of the dual polytopes of vertex transitive polytopes

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