# [R] Optimisation with Normalisation Constraint

Jeff Newmiller jdnewm|| @end|ng |rom dcn@d@v|@@c@@u@
Thu Jun 21 00:21:29 CEST 2018

```I recommend posting this on a mathematics discussion forum like Stack Exchange and (re-)reading the Posting Guide for this mailing list.

I think you are going to need to re-write your model function to algebraically combine your original model along with the constraint, and then use the original model alone for prediction... but I haven't tried it so might be quite far off the mark.

On June 20, 2018 8:50:48 AM PDT, Lorenzo Isella <lorenzo.isella using gmail.com> wrote:
>Dear All,
>I have a problem I haver been struggling with for a while: I need to
>carry out a non-linear fit (and this is the
>easy part).
>I have a set of discrete values {x1,x2...xN} and the corresponding
>{y1, y2...yN}. The difficulty is that I would like the linear fit to
>preserve the sum of the values y1+y2+...yN.
>I give an example below (for which there may even be an analytical
>solution, but that is not the point here)
>
>############################################################################
>library(minpack.lm)
>
>
>
>set.seed(124)
>
>z <- rexp(3000,3)
>
>
>zf <- z[z<= 0.5 | z>=0.9]
>
>myhist <- hist(zf, plot=FALSE)
>
>
>
>df <- data.frame(x=myhist\$mids, y=myhist\$density)
>
>
>
>myfit <- nlsLM(y~(A*exp(-lambda*x))
>                ,data=df, start=list(A=1,lambda=1))
>
>
>
>> sum(myhist\$density)
>[1] 5
>> sum(predict(myfit))
>[1] 4.931496
>
>############################################################################
>I would like sum(predict(myfit)) to be exactly 5 from the start,
>without renormalising a posteriori the fit.
>
>Any suggestion is appreciated.
>Cheers
>
>Lorenzo
>
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