[R] Bad optimization solution

[Paul Smith]

On 5/7/07, apjaworski at mmm.com <apjaworski at mmm.com> wrote:
> I think the problem is the starting point.  I do not remember the details
> of the BFGS method, but I am almost sure the (.5, .5) starting point is
> suspect, since the abs function is not differentiable at 0.  If you perturb
> the starting point even slightly you will have no problem.
>
>              "Paul Smith"
>              <phhs80 at gmail.com
>              >                                                          To
>              Sent by:                  R-help <r-help at stat.math.ethz.ch>
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>              at.math.ethz.ch
>                                                                    Subject
>                                        [R] Bad optimization solution
>              05/07/2007 04:30
>              PM
>
>
>
>
>
>
>
>
> Dear All
>
> I am trying to perform the below optimization problem, but getting
> (0.5,0.5) as optimal solution, which is wrong; the correct solution
> should be (1,0) or (0,1).
>
> Am I doing something wrong? I am using R 2.5.0 on Fedora Core 6 (Linux).
>
> Thanks in advance,
>
> Paul
>
> ------------------------------------------------------
> myfunc <- function(x) {
>   x1 <- x[1]
>   x2 <- x[2]
>   abs(x1-x2)
> }
>
> optim(c(0.5,0.5),myfunc,lower=c(0,0),upper=c(1,1),method="L-BFGS-B",control=list(fnscale=-1))

Yes, with (0.2,0.9), a correct solution comes out. However, how can
one be sure in general that the solution obtained by optim is correct?
In ?optim says:

     Method '"L-BFGS-B"' is that of Byrd _et. al._ (1995) which allows
     _box constraints_, that is each variable can be given a lower
     and/or upper bound. The initial value must satisfy the
     constraints. This uses a limited-memory modification of the BFGS
     quasi-Newton method. If non-trivial bounds are supplied, this
     method will be selected, with a warning.

which only demands that "the initial value must satisfy the constraints".

Paul