[R] Seeking optimal mixture
kari.ruohonen at saunalahti.fi
Wed Sep 26 15:37:06 CEST 2001
This is maybe not directly an R problem but I have used R to try to solve
it so I think somebody may be able to help.
I have a mixture model with three components and a quadratic Scheffe
polynomial p1x1+p2x2+p3x3+p12x1x2+p13x1x3+p23x2x3 fitted to the response.
Now I'd like to compute the mixture corresponding the maximum response.
Model for Y1 has the parameters
Solving a system of linear equations (solve(A,b)) of the partial derivates
and putting a constraint of x1+x2+x3=1 with Lagrange's multiplier finds
that produces the maximum response 130.378 within the experimental region.
Now, my model for another response Y2 has the parameters
Solving as above with the partial derivatives gives
that produces Y2(max)=44.381. But this is not the maximum since e.g.
produces 48.089 (but is not necessarily the maximum response).
I have looked at optim() and wondered if I could use it somehow to solve
my problem. However, I have not found a way to tell optim() about my sum
constraint x1+x2+x3=1. All help is appreciated.
Finnish Game and Fisheries Research Institute
Socioeconomic and Aquaculture Research
Turku Game and Fisheries Research
Itäinen Pitkäkatu 3, 20520 Turku, Finland
tel. +358-20-5751681, +358-40-5238321 (mobile)
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