# Questions tagged [convex-hulls]

For questions on the convex hull of a set, a set $X$ of points in a Euclidean space which is the smallest convex set that contains $X$. Consider adding (convex-analysis), or, for questions related to algorithms, (computational-geometry) and/or (discrete-geometry).

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### Given a set of points forming a convex hull, is it possible to find a specific hyperplane?

I have a set of points in $\mathbb{R}^n$ and I can use some convex hull algorithm to find the convex hull of this set and the corresponding extreme points (vertices). My goal is to find the supporting ...
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### Convex hull of a set is equivalent to the convex hull of the extreme point of the set?

Assume $X$ is a compact set (not necessarily convex). If the following equality holds true? $$\text{Conv}(X)=\text{Conv}(\text{extr(X)})$$ where $\text{extr}$ means the extreme point of $X$. The ...
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### Minimum number of points to have a point inside every triangle formed by $n$ points

Place $n$ points in a general position on the plane. Call a set $S$ of any points stabbing if every triangle formed by the $n$ chosen points contains at least one point from $S$ in its interior. For ...
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### One-to-one Correspondence of Facets of a Polytope [closed]

If the facets of a polytope $A$ are in one-to-one correspondence with the members of a finite set $X$ and the facets of a polytope $B$ are also in one-to-one correspondence with the members of $X$ (ie....
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### Techniques for convex optimization over a vertex-representation of a polytope?

I have a convex optimization problem where the feasible region is defined as the convex hull of a set of vertices. Even though the vertex set is in the low dozens of points, finding the half-space (H-...
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### Question about Interior of $S^n_+$ (semi definite positive matrices)

I read this link Interior of $S^n_+$ (semi definite positive matrices) and I have a question about What would be the relative interior of $S^n_+$ I prove that $S^n_+$ it's a is a closed pointed convex ...
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### Proving that a given set defined by an inequality is convex

I want to prove that the convex hull of a region defined by the following inequality is convex: $$(y-z)^2 -4x w \geq 0$$, where $x + y + z + w = 1$ and $x, y, z, w \geq 0$. I tried using the Hessian ...
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### How to find the inscribed and circumscribed circles from convex region?

Let $\mathbf{P}(t)$ be a piecewise bezier curve of degree $p$, which defines a jordan curve in the plane such the interior region $D$ is convex. Question: How can I find the external $C_e$ and ...
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### Is there such a thing as a convex polytope defined over a mixed-variable space: $\mathbb{Z}^m \times \mathbb{R}^n$

I am currently learning about polytopes and I have reached the stage of convex polytopes. Wiki says that a convex polytope is a special case of a polytope, having the additional property that it is ...
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