[R] optim with gradient

[ripley@stats.ox.ac.uk]

On Wed, 20 Mar 2002, [iso-8859-1] 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."

Only if hessian=FALSE, and that phrase is now removed.

> 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.

No, the other way around.  It meant `if gr is called, it will be called
...'


> 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.

You need to cache the par values and the results you need, and test both.
It is unlikely to be worth it.

>
> 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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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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