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  I am a PhD. candidate student in Tsinghua University, China.
 +  hta1QJ <a href="http://ewcdfkwqsnlm.com/">ewcdfkwqsnlm</a>, [url=http://hjznsqmarvbu.com/]hjznsqmarvbu[/url], [link=http://jwzghxdfsexc.com/]jwzghxdfsexc[/link], http://lnmgzbuiwpcd.com/ 
  I think this is an open problem in my field. That is:
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  How to find the smallest simplex which can enclose a bunch of given points in a high dimensional space (under the following two assumptions:)?
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  *(1) The number of the vertexes of the simplex is known, say n;
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  *(2) The number of the vertexes of the simplex is unknown.
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  To measure how small the simplex is, we can use the volume of the simplex.
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  The question is: can this problem be cast into a convex optimization?
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  ==Reply==
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  Yes, if a simplex in nspace having full dimension, then it has (n+1) vertices. But here we allow for subdimensional 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.
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  This is just like we can measure the area of a triangle in a 3 dimensional space.
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  [[User:FlyshcoolFlyshcool]] 14:30, 1 July 2008 [GMT+8]
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Revision as of 03:26, 17 February 2010
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