[R] R_using non linear regression with constraints

Bert Gunter bgunter.4567 at gmail.com
Sun Jun 18 19:29:52 CEST 2017

https://cran.r-project.org/web/views/Optimization.html

(Cran's optimization task view -- as always, you should search before posting)

In general, nonlinear optimization with nonlinear constraints is hard,
and the strategy used here (multiplying by a*b < 1000) may not work --
it introduces  a discontinuity into the objective function, so
gradient based methods may in particular be problematic.  As usual, if
either John Nash or Ravi Varadhan comment, heed what they suggest. I'm
pretty ignorant.

Cheers,
Bert

Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Sun, Jun 18, 2017 at 9:43 AM, David Winsemius <dwinsemius at comcast.net> wrote:
>
>> On Jun 18, 2017, at 6:24 AM, Manoranjan Muthusamy <ranjanmano167 at gmail.com> wrote:
>>
>> I am using nlsLM {minpack.lm} to find the values of parameters a and b of
>> function myfun which give the best fit for the data set, mydata.
>>
>> mydata=data.frame(x=c(0,5,9,13,17,20),y = c(0,11,20,29,38,45))
>>
>> myfun=function(a,b,r,t){
>>  prd=a*b*(1-exp(-b*r*t))
>>  return(prd)}
>>
>> and using nlsLM
>>
>> myfit=nlsLM(y~myfun(a,b,r=2,t=x),data=mydata,start=list(a=2000,b=0.05),
>>                  lower = c(1000,0), upper = c(3000,1))
>>
>> It works. But now I would like to introduce a constraint which is a*b<1000.
>
> At the moment your coefficients do satisfy that constraint so that dataset is not suitable for testing. A slight modification of the objective function to include the logical constraint as an additional factor does not "break" that particular solution.:
>
> myfun2=function(a,b,r,t){
>     prd=a*b*(1-exp(-b*r*t))*(a*b<1000)
>     return(prd)}
>
>
> myfit=nlsLM(y~myfun2(a,b,r=2,t=x),data=mydata,start=list(a=2000,b=0.05),
>             lower = c(1000,0), upper = c(3000,1))
>
> #------------------
> myfit
> Nonlinear regression model
>   model: y ~ myfun2(a, b, r = 2, t = x)
>    data: mydata
>         a         b
> 3.000e+03 2.288e-02
>  residual sum-of-squares: 38.02
>
> Number of iterations to convergence: 8
> Achieved convergence tolerance: 1.49e-08
> #--
>
> prod(coef(myfit))
> #[1] 68.64909  Same as original result.
>
> How nlsLM will handle more difficult problems is not something I have experience with, but obviously one would need to keep the starting values within the feasible domain. However, if your goal was to also remove the upper and lower constraints on a and b, This problem would not be suitably solved by the a*b product without relaxation of the default maxiter:
>
>> myfit=nlsLM(y~myfun2(a,b,r=2,t=x),data=mydata,start=list(a=2000,b=0.05),
> +             lower = c(0,0), upper = c(9000,1))
>> prod(coef(myfit))
> [1] 110.4382
>> coef(myfit)
>            a            b
> 9.000000e+03 1.227091e-02
>
>>  myfit=nlsLM(y~myfun2(a,b,r=2,t=x),data=mydata,start=list(a=2000,b=0.05),
> +              lower = c(0,0), upper = c(10^6,1))
> Warning message:
> In nls.lm(par = start, fn = FCT, jac = jac, control = control, lower = lower,  :
>   lmdif: info = -1. Number of iterations has reached `maxiter' == 50.
>
> #---------
>  myfit=nlsLM(y~myfun2(a,b,r=2,t=x),data=mydata,start=list(a=2000,b=0.05),
>              lower = c(0,0), upper = c(10^6,1), control=list(maxiter=100))
>  prod(coef(myfit))
>
>  coef(myfit)
> #============
>
>
>>  prod(coef(myfit))
> [1] 780.6732  Significantly different than the solution at default maxiter of 50.
>>
>>  coef(myfit)
>            a            b
> 5.319664e+05 1.467524e-03
>>
>>
>
>
> --
> David.
>
>
>> I had a look at the option available in nlsLM to set constraint via
>> nls.lm.control. But it's not much of help. can somebody help me here or
>> suggest a different method to to this?
>>
>>       [[alternative HTML version deleted]]
>>
>> ______________________________________________
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>> and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius
> Alameda, CA, USA
>
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