[R] optim with gradient

[Laurent Gautier]

On Wed, Mar 20, 2002 at 02:31:03PM +0100, Göran Broström wrote:
> I want to maximise a function using 'optim' with a method that requires 
> the gradient, so I supply two functions, 'fun' for the function value
> and 'd.fun' for its gradient. My question is: Since some calculations are 
> common to the two functions, is it possible to save time by feeding 
> 'd.fun' with some of the calculations made in 'fun'? That would require
> (at least) that it is guaranteed that each time 'd.fun' is evaluated, it 
> is done immediately after a call to 'fun' at the same parameter value.
> The help page says:  
> 
> "It is guaranteed that `gr' will be called immediately after a
> call to `fn' at the same parameter values."
> 
> which is not exactly the same. However, look at this trivial example:
> 
> prov <- function(x.start = 0){
>   fun <- function(x) {
>     e.x <- exp(-x)
>     x * e.x
>   }
>   d.fun <- function(x) {
>     e.x <- exp(-x)
>     e.x * (1 - x)
>   }
>   optim(x.start, fun, d.fun, method = "BFGS", 
>      control = list(fnscale = -1))
> }
> 
> > prov(2)$counts
> function gradient 
>       19        9 
> 
> This contradicts the help page info, since that implies that the gradient 
> is called at least as many times as the function. 
> 
> Q1: What is the correct guarantee? Is it what I need?
> 
> Q2: If so, How do I share calculations between the two functions? In my 
>     trivial example, exp(-x) is calculated in both.
> 
> Thanks for any enlightenment! (Brian?)
> 
> Göran 
> -- 
>  Göran Broström                      tel: +46 90 786 5223
>  professor                           fax: +46 90 786 6614
>  Department of Statistics            http://www.stat.umu.se/egna/gb/
>  Umeå University
>  SE-90187 Umeå, Sweden             e-mail: gb at stat.umu.se
> 
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Here is a (proposal of) reply for Q2:

Storing and accessing the result of the 'shared calculation' in a given environment could be a workaround.


Hopin' it helps,



Laurent

 

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