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.

  • $\begingroup$ Your question is relevant to this post, stats.stackexchange.com/questions/54687/…, which is an interpretation of multiple regression in terms of hyperplane. $\endgroup$
    – semibruin
    Jul 22, 2013 at 22:40
  • $\begingroup$ @semibruin Thank you, but that question doesn't seem to be very relevant. $\endgroup$
    – S.B.
    Jul 22, 2013 at 22:52


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.