# Re: [R] Bad optimization solution

From: Paul Smith <phhs80_at_gmail.com>
Date: Mon, 07 May 2007 23:21:48 +0100

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>
> r-help-bounces_at_st cc
> at.math.ethz.ch
> Subject
> 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).
>
>
> 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

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