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I asked the following question on Math.SE and I've been told that I may get more helpful answers here on Cross Validated. This is my first question here, so I hope the tags I've chosen are accurate enough.

Let $S$ be a $k$-simplex in $\mathbb{R}^k$. I'd like to find a hyperplane $P$ that passes through the origin such that projections of vertices of $S$ onto $P$ are as close as possible to the origin (in minimax sense). The distances are measured in $\ell_2$-norm.

I could only get trivial results for $k=2$, but even for $k=3$ I couldn't find a way to find a solution.

Any hint on whether there is a polynomial-time algorithm that can solve this would be appreciated. If you know papers that are relevant I'd be thankful if you let me know.

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S.B.
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  • Your question is relevant to this post, http://stats.stackexchange.com/questions/54687/how-can-a-vector-of-variables-represent-a-hyperplane, which is an interpretation of multiple regression in terms of hyperplane. – semibruin Jul 22 '13 at 22:40
  • @semibruin Thank you, but that question doesn't seem to be very relevant. – S.B. Jul 22 '13 at 22:52

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