scaling problems in "optim"

ALL: 

      Can anyone explain why optim returns c(0.75, 2) for what I think 
should be the maximum of a bivariate normal density with mean = 1:2? 


KATHIE: 

      Apart from 'optim' giving an answer I don't understand, the 
following should illustrate the use of 'fnscale' and 'parscale' -- while 
perhaps illustrating the need to use these parameters. 

      Hope this helps. 
      Spencer Graves

library(mvtnorm)
(mle2 <- optim(rep(0, 2), dmvnorm, method='CG',
               control=list(fnscale=-10, parscale=c(.3, 3), trace=9),
              mean=1:2, hessian=TRUE, log=TRUE))
  Conjugate gradients function minimizer
Method: Fletcher Reeves
tolerance used in gradient test=3.63798e-12
0 1 0.433788
parameters    0.00000    0.00000
 i> 1 3 0.234892
parameters    0.03000    0.60000

<snip>

i> 100 201 0.187167
parameters    2.46674    0.66667
$par
[1] 0.7352784 2.0000004 # = approximately c(2.46674, 0.66667) * parscale

$value
[1] -1.871671 # = 0.187167 * fnscale

$counts
function gradient
     201      101

$convergence
[1] 1

$message
NULL

$hessian
             [,1]         [,2]
[1,] -1.00000e+00 -9.94586e-11
[2,] -9.94586e-11 -1.00000e+00

# Checks:  

 > dmvnorm(c( 0.7352784, 2.0000004), mean=1:2, log=TRUE)

[1] -1.872916

 > dmvnorm(1:2, mean=1:2, log=TRUE)

[1] -1.837877
 

kathie wrote:
  

Dear R users,

I am trying to figure out the control parameter in "optim,"  especially,
"fnscale" and "parscale."

In the R docu.,

------------------------------------------------------
fnscale

    An overall scaling to be applied to the value of fn and gr during
optimization. If negative, turns the problem into a maximization problem.
Optimization is performed on fn(par)/fnscale.

parscale

    A vector of scaling values for the parameters. Optimization is performed
on par/parscale and these should be comparable in the sense that a unit
change in any element produces about a unit change in the scaled value.
------------------------------------------------------

I cannot understand these two statements.

"Optimization is performed on fn(par)/fnscale." and

"Optimization is performed on par/parscale and these should be comparable in
the sense that a unit change in any element produces about a unit change in
the scaled value."

Would you please explain these things?  

Thank you in advance.

Kathryn Lord