[R] Minimizing two non-linear functions with genoud - Trying to minimize or converge near zero

[Guillaume Théroux Rancourt]

Thank you Ravi!

What I forgot to mention in my first post is that gi should be between [0,1], while Vcmax is usually between [0,150], but can be higher [0,250]. That was the Domains of the genoud function initially.

Also, in this example, f.1 should equal 7.478 and f.2 = 12.731 with the same Vcmax and gi.

Using optim, I see that it is very sensitive to the starting parameters. Using c(0.15, 100) give parameters close to what should be expected, but it is still not close enough to 7.478 for f.1 (for example).

Thank you for your help,

Guillaume

> I do not understand completely what you are trying to do, but may be this works for you!?
> 
> f=function(x) { 
> 
> # x = c(0.16,80)
> Vcmax = x[2]
> gi = x[1]
> 
> # First dataset
> f.1=function(x){
> (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
> }
> 
> # Second data set
> f.2=function(x){
> (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)
> }
> 
> # Values here are the measured values. f.1 and f.2 should be equal or close to the value on their left.
> y.1 = abs(7.478327 - f.1(x))
> y.2 = abs(12.73134 - f.2(x))
> 
> # This should be close to 0.
> y = (y.1 - y.2)^2
> 
> return(y*y)
> }
> 
> dom = matrix(c(0,0,200,1.5), 2, 2)
> 
> res <-  optim(par=c(0.15,100), fn=f, method="BFGS")  # no need for "genoud" here
> 
> # First dataset
> f.1=function(x){
> Vcmax = res$par[1]
> gi = res$par[2]
> (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
> }
> 
> # Second data set
> f.2=function(x){
> Vcmax = res$par[1]
> gi = res$par[2]
> (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)
> }
> 
> 
> f.1(res$par)
> f.2(res$par)
> 
> 
> Hope this is helpful,
> Ravi.
> 
> ____________________________________________________________________
> 
> Ravi Varadhan, Ph.D.
> Assistant Professor,
> Division of Geriatric Medicine and Gerontology
> School of Medicine
> Johns Hopkins University
> 
> Ph. (410) 502-2619
> email: rvaradhan at jhmi.edu
> 
> 
> ----- Original Message -----
> From: Guillaume Théroux Rancourt <Guillaume.Theroux-Rancourt at fsaa.ulaval.ca>
> Date: Thursday, February 4, 2010 3:02 pm
> Subject: [R] Minimizing two non-linear functions with genoud - Trying to minimize or converge near zero
> To: "r-help at r-project.org" <r-help at r-project.org>
> 
> 
>> Hello R users,
>> 
>> I am trying to minimize two functions with genoud. It is actually one 
>> function with two sets of data, each of them having two unknown 
>> variables (called Vcmax and gi) which have the same value in each of 
>> the function. They are called f.1 and f.2 in the code below.
>> 
>> My objective to minimize the functions in order to get the two 
>> variables equal in each of the functions. Furthermore, I have a 
>> measured comparison value for each of the function expression, and the 
>> results of f.1 and f.2 should be very close or equal to their measured 
>> value, so that  measured.1 - f.1 = 0.
>> 
>> I have been able to run genoud with the code below. However, I 
>> haven't been able to restrain the values of the difference between the 
>> measured and estimated value to 0. I am fairly new at writing R 
>> functions and I think there might be something I haven't written that 
>> makes the output parameters of genoud not replicable.
>> 
>> I have made several runs of this function and when comparing with the 
>> measured value, I got answers between 1 and 12, where it should have 
>> been very close to 7.47.
>> 
>> This example has already been solved with the solver Excel add-in and 
>> theh result are:
>> Vcmax = 104.32, gi = 0.11
>> 
>> The values were also estimated using another approach and they are:
>> Vcmax = 64.48, gi = 0.28
>> 
>> 
>> Here is my code. 
>> 
>> 
>> ######
>> 
>> f=function(x) { 
>> 
>> x = c(0.16,80)
>> Vcmax = x[2]
>> gi = x[1]
>> 
>> # First dataset
>> f.1=function(x){
>> (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
>> }
>> 
>> # Second data set
>> f.2=function(x){
>> (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)
>> }
>> 
>> # Values here are the measured values. f.1 and f.2 should be equal or 
>> close to the value on their left.
>> y.1 = (7.478327 - f.1(x))
>> y.2 = (12.73134 - f.2(x))
>> 
>> # This should be close to 0.
>> y = y.1 - y.2
>> 
>> return(y)
>> }
>> 
>> dom = matrix(c(0,0,200,1.5), 2, 2)
>> 
>> res = genoud(f, nvars=2, max=FALSE,Domains=dom,pop.size=5000,print.level=0)
>> 
>> 
>> # In order to test the results to see I the estimated variables make 
>> the "test" function = 7.478327 or near.
>> # This is the same as f.1
>> 
>> test=function(Vcmax, gi){
>> (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
>> }
>> 
>> test(res$par[1],res$par[2])
>> 
>> ## End 
>> 
>> 
>> Thank you for your help!
>> 
>> 
>> Guillaume Théroux Rancourt
>> Ph.D. candidate --- Plant Biology
>> Université Laval, Québec, QC, Canada
>> guillaume.theroux-rancourt.1 at ulaval.ca
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list
>> 
>> PLEASE do read the posting guide 
>> and provide commented, minimal, self-contained, reproducible code.