[R] Supply linear constrain to optimizer

[Philippe Grosjean]

>Prof Brian Ripley <ripley at stats.ox.ac.uk> writes:

>> If the boundary cases were of interest it would be nice to have an
>> optimizer that allows linear inequality bounds (that is to optimize over
a
>> simplex).

>Anyone looking for a project? I don't actually think this is
>particularly hard to do for someone who understands what the
>box-constrained algorithm already does. (That is a nearly vacuous
>statement, I know. Brian would be eligible, but hardly looking for a
>project...).

I have unfortunately absolutely *no* time (a PhD thesis and a R
package -PASSTEC- to finish for the end of the year), but I am _very, very_
interested by such a feature in R! A good starting place in the litterature:
Nocedal & Wright, 1999. Numerical optimization. Spriger, New York: chapters
12 & 13. A starting point in GPL code? Don't know, may be is it something
like this in Octave or Scilab???
Best,

Philippe Grosjean

>There are two approaches: Either allow the box to generalize into
>arbitrary intersections of half-spaces (I don't think that's the
>definition of a simplex?) , or allow linear *equality* restrictions to
>be added to the original optimization problem, so that you could

>max f(c1,c2,c3) subj. to
>c3 == c1 + c2
>with constr.
>0 < c1 < 1
>0 < c2 < 1
>c3 < 1

>--
>   O__  ---- Peter Dalgaard             Blegdamsvej 3
>  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
> (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
>~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

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