[R] optim with gradient

[Adrian Trapletti]

> Date: Wed, 20 Mar 2002 14:31:03 +0100 (CET)
> From: =?iso-8859-1?Q?G=F6ran_Brostr=F6m?= <gb at stat.umu.se>
> Subject: [R] optim with gradient
>
> 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
>

If the only goal is to improve speed, then you should consider to do the full optimization within C/Fortran, i.e., to implement the errfunc and the gradient in C and to call optim through the API (a new feature of the upcoming version 1.5.0 as Brian told me). This may increase speed - I just make a rough guess now - by a factor 100.

best
Adrian


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