# Smallest simplex

(Difference between revisions)
 Revision as of 22:34, 30 June 2008 (edit)← Previous diff Revision as of 15:48, 5 March 2009 (edit) (undo)Next diff → Line 10: Line 10: The question is: can this problem be cast into a convex optimization? The question is: can this problem be cast into a convex optimization? + ==question== ''Doesn't a simplex in n-space always have (n+1) vertices (http://en.wikipedia.org/wiki/Simplex)? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?'' ''Doesn't a simplex in n-space always have (n+1) vertices (http://en.wikipedia.org/wiki/Simplex)? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?''

## Revision as of 15:48, 5 March 2009

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?

## question

Doesn't a simplex in n-space always have (n+1) vertices (http://en.wikipedia.org/wiki/Simplex)? Or would you want to allow for sub-dimensional simplices? But then, measuring the volume is quite pointless for all but the full-dimensional ones. I'm probably misunderstanding something, perhaps you can clarify this?