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# Questions tagged [convex-geometry]

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### Approximating the diameter of a convex set defined by semidefinite constraints

A convex subset $C$ of $\mathbb{R}^{n^2}$ is given as the set of positive semidefinite $n\times n$ matrices whose coefficients fulfill some affine equations. Now, if you want to minimize a linear ...
259 views

### Intersection of Hamming Balls

I am interested in the volume of the intersection of two Hamming balls of radius say m/6 in m-dimensional space, the distance between whose centers is about \sqrt{m}. I would ideally like this to be a ...
123 views

### Equivalence of weighted Minkowski sums

Given $n$ polytopes $P_1, \cdots, P_n$, each $P_i$ is given as the V-representation, i.e., a set of $m$ points as its set of vertices. Furthermore, consider a variant of the Minkowski sum (somehow ...
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### Computing the convex hull of several polyhedra

Let $K_1,..., K_m$ be a set of $m$ polyhedra, with $K_i\subseteq \mathbf{R}^n$, for all $i\in [m]$, and each is described by a set of $poly(n)$ linear inequalities. How easy is it to compute an ...
148 views

### Is the following problem in $coNP$?

Given an $n\times n$ matrix $M$ with $\mathbb Z$ entries is 'does an $\frac n2\times\frac n2$ minor of $M$ vanish?' in $\bf{coNP}$? At least one $\frac n2\times\frac n2$ minor non-vanish implies rank ...
1 vote
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### How can we prove what the shortest line between two points avoiding convex obstacles is? (visibility graphs)?

I came across the observation in russell & norvig's artificial intelligence book that the shortest path between two points while avoiding convex polygonal obstacles is a sequence of line segments ...
1 vote
Given a linear integer program $Ax\leq b$ with $A\in\mathbb Z^{m\times n}$ and $b\in\mathbb Z^m$ known is there a polynomial time algorithm to give tight upper bounds for $\log_2\|x\|_\infty$ and $\... 1 vote 0 answers 130 views ### Hausdorff Distance and Convex Hull Given two sets of points A and B, both in$R^d$, is there a relation between the convex hulls of A and B, i.e. conv(A) and conv(B), w.r.t. the Hausdorff distance between A and B? In other words, does ... 1 vote 0 answers 85 views ### Compute basis of vertex set of polytope I am wondering whether there is an efficient algorithm to compute the basis of the set of vertices of a polytope. Formally, INPUT: a polytope$$\Xi=\{(\vec{a}_1\vec{x}+\vec{b}_1, \cdots, \vec{a}_m\... 1 vote 0 answers 135 views ### Orlicz Norm and a result on expectation I am reading a paper which is mainly about Dobrushin's contraction coefficient and its generalization. In page 27, the following is defined: Consider an arbitrary, non-negative, convex function$\psi:\...
An extended formulation (EF) of a polytope $P\subseteq \mathbb{R}^d$ is a system of linear constraints $Ex + Fy = g, y\geq 0$ in variables $(x,y)\in \mathbb{R}^{d+r}$ where $E,F$ are real matrices ...