[R] optim, constrOptim: setting some parameters equal to each other

[Katharine Mullen]

Here is an example w/optim where you have an objective function
F(x) where you have (possibly a few) constraints of form x_i=x_j, and you
can specify the constraints flexibly, which is what I _think_ you want.
An example from you would have been nice.

## objective function that depends on all parameters, here a, b, c
obfun <- function(a,b,c,dd)
    sum((dd - (exp(a * 1:100) + exp(b * 1:50) + exp(c * 1:25) ))^2)

## fn for optim
fr <- function(x, eqspec, dd, obfun) {
  ## assign variables for parameter values given in x
  for(i in 1:length(x))
    assign(names(x)[i], x[[i]])
  ## use eqspec to assign parameter values determined w/equ. constr.
  for(i in 1:length(eqspec))
    assign( names(eqspec)[i], x[[ eqspec[[i]] ]])
  ## now have all parameter values, call objective function
  obfun(a,b,c,d, dd)
}

dd <- exp(-.05 * 1:100) + exp(-.05 * 1:50) + exp(.005 * 1:25)

## let par contain all parameters that are not eq. constrained and
## all parameters on right side of constraints of form a=b

## let eqspec give all dependent parameters on left side of
## the constraints of form a=b

## e.g.
## for constraint a=b
xx <- optim(par=list(b=-4, c=-.1), fn=fr, eqspec=list(a="b"),
            dd=dd, obfun=obfun)

## for constraint b=a
x1 <- optim(par=list(a=-4, c=-.1), fn=fr, eqspec=list(b="a"),
            dd=dd, obfun=obfun)

On Sun, 8 Jun 2008, Alex F. Bokov wrote:

> Hello, and apologies for the upcoming naive questions. I am a biologist
> who is trying to teach himself the appropriate areas of math and stats.
> I welcome pointers to suggested background reading just as much as I do
> direct answers to my question.
>
> Let's say I have a function F() that takes variables (a,b,c,a1,b1,c1)
> and returns x, and I want to find the values of these variables that
> result in a minimum value of x. That's a straightforward application of
> optim(). However, for the same function I also need to obtain values
> that return the minimum value of x subject to the following constraints:
> a=a1, b=b1, c=c1, a=a1 && b=b1, a=a1 && c=c1, ... and so on, for any
> combination of these constraints including a=a1, b=b1, c=c1. The brute
> force way to do this with optim() would be to write into F() an immense
> switch statement anticipating every possible combination of constrained
> variables. Obviously this is inefficient and unmaintainable. Therefore,
> my question is:
>
> Is the purpose of constrOptim() this exact type of problem? If so, how
> does one express the constraint I described above in terms of the ui,
> ci, and theta parameters? Are there any introductory texts I should have
> read for this to be obvious to me from constrOptim's documentation?
>
> If constrOptim() is not the answer to this problem, can anybody suggest
> any more elegant alterntives to the switch-statement-from-hell approach?
>
> Thank you very, very much in advance. I thought I understood R
> reasonably well until I started banging my head against this problem!
>
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