# [R] optim bug/help?

Patrick Burns pburns at pburns.seanet.com
Thu Oct 23 22:16:06 CEST 2008

```rkevinburton at charter.net wrote:
> I was just trying to get a feel for the general strengths and weaknesses of the algoritmns. This is obviously a "demo" function and probably not representative of the "real" optimization problems that I will face. My concern was that if there is inaccuracy when I know the answer it might be worse when I don't if I don't understand the characteristics of the algoritmns involved.
>

One approach to this problem is to do the optimization
several times with different (random?) starts.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")
> Kevin
>
> ---- Ben Bolker <bolker at ufl.edu> wrote:
>
>>  <rkevinburton <at> charter.net> writes:
>>
>>
>>> In the documentation for 'optim' it gives the following function:
>>>
>>> fr <- function(x) {   ## Rosenbrock Banana function
>>>     x1 <- x[1]
>>>     x2 <- x[2]
>>>     100 * (x2 - x1 * x1)^2 + (1 - x1)^2
>>> }
>>> optim(c(-1.2,1), fr)
>>>
>>> When I run this code I get:
>>>
>>> \$par
>>> [1] 1.000260 1.000506
>>>
>>> I am sure I am missing something but why isn't 1,1 a better answer? If I plug
>>>
>> 1,1 in the function it seems that
>>
>>> the function is zero. Whereas the answer given gives a function result of
>>>
>> 8.82e-8. This was after 195 calls
>>
>>> to the function (as reported by optim). The documentation indicates that the
>>>
>> 'reltol' is about 1e-8. Is
>>
>>> this the limit that I am bumping up against?
>>>
>>> Kevin
>>>
>>>
>>   Yes, this is basically just numeric fuzz, the
>> bulk of which probably comes from finite-difference
>> evaluation of the derivative.
>> As demonstrated below, you can get a lot closer
>> by defining an analytic gradient function.
>> May I ask why this level of accuracy is important?
>> to the right question here ...)
>>
>>   Ben Bolker
>> ---------
>>
>> fr <- function(x) {   ## Rosenbrock Banana function
>>     x1 <- x[1]
>>     x2 <- x[2]
>>     100 * (x2 - x1 * x1)^2 + (1 - x1)^2
>> }
>>
>> frg <- function(x) {
>>   x1 <- x[1]
>>   x2 <- x[2]
>>   c(100*(4*x1^3-2*x2*2*x1)-2+2*x1,
>>     100*(2*x2-2*x1^2))
>> }
>>
>> ## use numericDeriv to double-check my calculus
>> x1 <- 1.5
>> x2 <- 1.7
>> numericDeriv(quote(fr(c(x1,x2))),c("x1","x2"))
>> frg(c(x1,x2))
>>
>> ##
>> optim(c(-1.2,1), fr,method="BFGS")
>> optim(c(-1.2,1), fr, gr=frg,method="BFGS")  ## use gradient
>>
>> ______________________________________________
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>> https://stat.ethz.ch/mailman/listinfo/r-help
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
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