R help - Jun 2009 - Curve fit a nonlinear equation with box constraints: success, many thanks!

Dear R Helper Community!

 

Thank you for all your help and suggestions.  

For your reference and any future person searching the archives, here is the
solution that did what I wanted it to do.

 

As background, my goal was to find the coefficients for the following
equation form:

y ~ c1 * x1 * x2 ^ -c2 *x3 ^ c3

where y, x1, x2, and x3 are observed data, and

c1, c2 and c3 are regression coefficients subject to the following
constraints:

0.0   <= c2 <= 1.0

0.0   <= c3 <= 1.0

 

I ran the following code as a script from the R Gui on a windows machine.

The command for this was: 
source("C:\\Users\\me\\R281\\work\\optimcall.R")

 

# **** Script file: optimcall.R ***********

# function definition

rss <- function(par) {

  y <-
c(0.111111111111111,0.0921052631578947,0.0564516129032258,0.0608108108108108
,0.0128205128205128,0.0136078431372549)

  x1 <-
c(0,0.978723404255319,0.087378640776699,0.549295774647887,0.0596026490066225
,0.61578947368421)

  x2 <- c(1,3,4,5,6,7)

  x3 <- c(3600,169200,185400,255600,271800,342000)

  par1 <- par[1]

  par2 <- par[2]

  par3 <- par[3]

  ressq <- (y - par1 * (x1 + 1) * x2^(-par2) * x3^par3)^2

  sum(ressq)

 }

 

#call to optimizer

opti <- optim(c(0.5, 0.5, 0.1), rss, gr = NULL, method =
"L-BFGS-B", lower c(-Inf, 0, 0), upper = c(Inf, 1, 1) )

#  ***** End script file *********

 


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