Smallest simplex

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Revision as of 03:26, 17 February 2010

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-I am a PhD. candidate student in Tsinghua University, China.
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-I think this is an open problem in my field. That is:
-How to find the smallest simplex which can enclose a bunch of given points in a high dimensional space (under the following two assumptions:)?
-*(1) The number of the vertexes of the simplex is known, say n;
-*(2) The number of the vertexes of the simplex is unknown.
-To measure how small the simplex is, we can use the volume of the simplex.
-The question is: can this problem be cast into a convex optimization?
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-==Reply==
-Yes, if a simplex in n-space having full dimension, then it has (n+1) vertices. But here we allow for sub-dimensional simplexes. I don't think measuring the volume of them is pointless if we constrain our focus to the sub affine set where the simplex resides.
-This is just like we can measure the area of a triangle in a 3 dimensional space.
---[[User:Flyshcool|Flyshcool]] 14:30, 1 July 2008 [GMT+8]