Re: [Rd] Minor glitch in optim()

[Martin Maechler]

> J C Nash 
> on Tue, 17 Apr 2018 10:18:02 -0400 writes:

> 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.

I agree that it inconsistent.  The help page mentions that
"non-trivial" bounds are treated like that, and if you'd
consider  lower = c(-Inf, -Inf) to be  "non-trivial",  one could
say optim() behaved according to documentation and non-buggy,
but a much more reasonable definition of non-trivial bounds are
bounds that are not equivalent to (lower=-Inf, upper=+Inf)  and
the vector versions *are* equivalent.

So I agree about fixing.

> 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.

I agree.  

> 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

I aim to go for the first line

if((any(lower > -Inf)) || any(upper < Inf))

which is 100% correct and easier to "read", even though your
version -- after adding the missing ')' -- is faster
 and almost always equivalent.

Running checks now.  Wont' be in R 3.5.0 of course,  but then
probably in  R 3.5.0 patched.

Martin Maechler
ETH Zurich

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[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

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