[R] optim

[Duncan Murdoch]

nwew wrote:
> Dear R-helpers,
> 
> The function optim implements algorithms that I would like to use.
> 
> 
> I have function implemented in R, which given the parameters of which 
> minimization is to take place returns a scalar as well as the gradient.
> 
> Unfortunately optim requires two function _fn_ and _gr_ where fn returns the 
> function value and gr the gradient. Splitting my function in two functions 
> would be easy, however I am wondering if evaluating both is not doubling the 
> the very high computational costs. Most of the computational intensive 
> operations are identical if computing the function value and gradient.
> 
> Question: is there a way to tweek optim that only one function evaluation is 
> necessary? Are ther other implementations of the algorithm, which do assume 
> that the function to be minimized returns the function value and the gradient 
> as well?

I don't know the answer to your question, but here's a different 
approach.  Write a function that effectively splits your single function 
into two:

splitfn <- function(f) {
   lastx <- NA
   lastfn <- NA
   lastgr <- NA

   doeval <- function(x) {
     if (identical(all.equal(x, lastx), TRUE)) return(lastfn)
     lastx <<- x
     both <- f(x)
     lastfn <<- both$fnval
     lastgr <<- both$grval
     return(lastfn)
   }

   fn <- function(x) doeval(x)

   gr <- function(x) {
     doeval()
     lastgr
   }

   list(fn=fn, gr=gr)
}

I haven't tested this, but the idea is that it sets up a local 
environment where the last x value and last function and gradient values 
are stored.  If the next call asks for the same x, then the cached 
values are returned.  I don't know if it will actually improve 
efficiency:  that depends on whether optim evaluates the gradient and 
function values at the same points or at different points.

You would use this as follows, assuming your function is called f:

  f2 <- splitfn(f)

  optim(par, f2$fn, f2$gr, ...)

Duncan Murdoch