R help - Jan 2006 - Minimizing mahalanobis distance to negative orthant

Hi

I have the following problem: given x (px1) and S (pXp positive definite), find
y such that y_i<=0 (i=1..p) minimizing the
mahalanobis distance (x-y)'S^{-1}(x-y). 

Has anyone worked on this problem? Tips or R code would be appreciated.

David

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David Edwards
Principal scientist
Biostatistics

Novo Nordisk A/S
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On Thu, 19 Jan 2006, DED (David George Edwards) wrote:
> I have the following problem: given x (px1) and S (pXp positive 
> definite), find y such that y_i<=0 (i=1..p) minimizing the mahalanobis 
> distance (x-y)'S^{-1}(x-y).
>
> Has anyone worked on this problem? Tips or R code would be appreciated.
If I read this correctly (some spaces would help) you want

y such that y <= 0 and y minimizes (x-y)'Q(x-y) for a symmetric pos def
Q.

That is a quadratic program, so see package quadprog.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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