Smallest simplex
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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:)? | 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; | *(1) The number of the vertexes of the simplex is known, say n; | ||
| - | *(2) The number of the vertexes of the simplex is unknown | + | *(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. | 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? | The question is: can this problem be cast into a convex optimization? | ||
Revision as of 01:59, 12 June 2008
I am a PhD. candidate student in Tsinghua University, China. 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?