[R] Order of methods for optimx

[Marc Girondot]

Dear R-er,

For a non-linear optimisation, I used optim() with BFGS method but it 
stopped regularly before to reach a true mimimum. It was not a problem 
with limit of iterations, just a local minimum. I was able sometimes to 
reach better minimum using several rounds of optim().

Then I moved to optimx() to do the different optim rounds automatically 
using "Nelder-Mead" and "BFGS" methods

I find a huge time difference using system.time() based on the order of 
these both methods:

 > snb # "Nelder-Mead" and "BFGS"
     user   system  elapsed
1021.656    0.200 1021.695
 > sbn # "BFGS" and "Nelder-Mead"
     user   system  elapsed
3140.096    0.384 3139.728

But optimx() with "Nelder-Mead" and "BFGS" stops in local minimum:

 > o_mu2p1$value
[1] 2297.557

whereas "BFGS" and "Nelder-Mead" stops in better model (not sure if it 
is a global minimum, but it is better):

 > o_mu2p1$value
[1] 2297.305

####################

My questions are:

Are my findings common and documented (order of methods giving non 
consistant results) or are they specific to the model I try to fit ?

If it is known problem, where I can find the best advice about order of 
methods ?

####################

To reproduce what I said:

install.packages("http://www.ese.u-psud.fr/epc/conservation/CRAN/HelpersMG.tar.gz", 
repos=NULL, type="source")
install.packages("http://www.ese.u-psud.fr/epc/conservation/CRAN/phenology.tar.gz", 
repos=NULL, type="source")

library("phenology")
library("car")
library("optimx")
library("numDeriv")

ECFOCF_2002 <- TableECFOCF(MarineTurtles_2002)
snb <- system.time(
   o_mu2p1_nb <- fitCF(par = structure(c(0.244863062899293,
                                    43.5578630363601,
                                    4.94764539004454,
                                    129.606771856887,
                                    -0.323749593604171,
                                    1.37326091618759),
                                  .Names = c("mu1", "size1", "mu2",
                                             "size2", "p", "OTN")),
                  method = c("Nelder-Mead", "BFGS"),
                  data=ECFOCF_2002, hessian = TRUE)
)
sbn <- system.time(
   o_mu2p1_bn <- fitCF(par = structure(c(0.244863062899293,
                                      43.5578630363601,
                                      4.94764539004454,
                                      129.606771856887,
                                      -0.323749593604171,
                                      1.37326091618759),
                                    .Names = c("mu1", "size1", "mu2",
                                                "size2", "p", "OTN")),
                    method = c("BFGS", "Nelder-Mead"),
                    data=ECFOCF_2002, hessian = TRUE)
)

snb
o_mu2p1_nb$value

sbn
o_mu2p1_bn$value