Smallest simplex

From Wikimization

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?

To contact me, my E-mail address is: yuyue05@mails.tsinghua.edu.cn.