[Rd] Minor glitch in optim()

[J C Nash]

Having worked with optim() and related programs for years, it surprised me
that I haven't noticed this before, but optim() is inconsistent in how it
deals with bounds constraints specified at infinity. Here's an example:

# optim-glitch-Ex.R
x0<-c(1,2,3,4)
fnt <- function(x, fscale=10){
  yy <- length(x):1
  val <- sum((yy*x)^2)*fscale
}
grt <- function(x, fscale=10){
  nn <- length(x)
  yy <- nn:1
  #    gg <- rep(NA,nn)
  gg <- 2*(yy^2)*x*fscale
  gg
}

npar <- 4
lower <- -Inf
l2 <- rep(-Inf,npar)

a1 <- optim(x0, fnt, grt, lower=lower, method="BFGS") # works
a1
a1a<- optim(x0, fnt, grt, lower=l2, method="BFGS") # changes method!
a1a

The first call uses BFGS method without warning. The second gives
a warning that L-BFGS-B should be used, and from the output uses
this.

This is a bit of an edge case. My own preference would be for optim()
to simply fail if bounds of any type are specified without L-BFGS-B
as the method. I believe that gives clarity, even though infinite
bounds imply an unconstrained problem.

The behaviour where a scalar infinite bound is treated as unconstrained
but a vector is not is inconsistent, however, and I think that at some
point should be fixed. Possibly the easiest way is to treat infinite
bounds specified as a vector the same as those specified as a scalar.
That is to adjust the code in File src/library/stats/R/optim.R
in the block

    if((length(lower) > 1L || length(upper) > 1L ||
       lower[1L] != -Inf || upper[1L] != Inf)
       && !any(method == c("L-BFGS-B","Brent"))) {
	warning("bounds can only be used with method L-BFGS-B (or Brent)")
	method <- "L-BFGS-B"
    }

Possibly

    if((any(is.finite(lower) || any(is.finite(upper))
       && !any(method == c("L-BFGS-B","Brent"))) {
	warning("bounds can only be used with method L-BFGS-B (or Brent)")
	method <- "L-BFGS-B"
    }

Best, JN