From: Rolf Turner <rolf_at_erdos.math.unb.ca>

Date: Thu 10 Aug 2006 - 02:08:25 EST

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu Aug 10 02:12:01 2006

Date: Thu 10 Aug 2006 - 02:08:25 EST

Yingfu Xie wrote:

> I had problems with an extension to a classic optimization problem.

*>
**> The target is to minimize a quadratic form a'Ma with respect to vector
**> b, where vector a=(b',-1)', i.e., a is the expand of b, and M is a
**> symmetric matrix (positive definite if needed). One more constrain on b
**> is b'b=1. I want to solve b given M.
**>
**> I tried but it seems impossible to find an analytic solution for b. Any
**> objection?
**>
**> Now, come to the numerical. Does anybody have any idea on how to
**> parameterize this to use, e.g. optim() or constrOptim()?
**>
**> Any help are appreciated very much!
*

The analytic solution is trivial. Write M as

| M_11 c | | c' m | Then given that M_11 is positive definite, the minimizer is b = (M_11)^{-1}c cheers, Rolf Turner rolf@math.unb.ca ______________________________________________R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu Aug 10 02:12:01 2006

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.1.8, at Thu 10 Aug 2006 - 10:19:39 EST.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*