# Re: [R] Bad optimization solution

From: Jasjeet Singh Sekhon <sekhon_at_berkeley.edu>
Date: Tue, 08 May 2007 03:48:01 -0700

The issue is that you are using a derivative based optimizer for a problem for which it is well known that such optimizers will not perform well. You should consider using a global optimizer. For example, "rgenoud" combines a genetic search algorithm with a BFGS optimizer and it works well for your problem:

library(rgenoud)

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))

genoud(myfunc, nvars=2, Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2)

myfunc <- function(x) {
x1 <- x[1]
x2 <- x[2]
(x1-x2)^2
}

optim(c(0.2,0.2),myfunc,lower=c(0,0),upper=c(1,1),method="L-BFGS-B",control=list(fnscale=-1)) genoud(myfunc, nvars=2, Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2)

Cheers,
Jas.

```Jasjeet S. Sekhon

Associate Professor
Travers Department of Political Science
Survey Research Center
UC Berkeley

```

http://sekhon.berkeley.edu/
V: 510-642-9974 F: 617-507-5524

Paul Smith writes:
> It seems that there is here a problem of reliability, as one never
> knows whether the solution provided by R is correct or not. In the
> case that I reported, it is fairly simple to see that the solution
> provided by R (without any warning!) is incorrect, but, in general,
> that is not so simple and one may take a wrong solution as a correct
> one.
>
> Paul
>
>
> > Your function, (x1-x2)^2, has zero gradient at all the starting values such
> > that x1 = x2, which means that the gradient-based search methods will
> > terminate there because they have found a critical point, i.e. a point at
> > which the gradient is zero (which can be a maximum or a minimum or a saddle
> > point).
> >
> > However, I do not why optim converges to the boundary maximum, when analytic
> > gradient is supplied (as shown by Sundar).
> >
> > Ravi.
> >
> > ----------------------------------------------------------------------------
> > -------
> >
> >
> > Assistant Professor, The Center on Aging and Health
> >
> > Division of Geriatric Medicine and Gerontology
> >
> > Johns Hopkins University
> >
> > Ph: (410) 502-2619
> >
> > Fax: (410) 614-9625
> >
> >
> >
> >
> >
> > ----------------------------------------------------------------------------
> > --------
> >
> >
> > -----Original Message-----
> > From: r-help-bounces_at_stat.math.ethz.ch
> > [mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of Paul Smith
> > Sent: Monday, May 07, 2007 6:26 PM
> > To: R-help
> > Subject: Re: [R] Bad optimization solution
> >
> > On 5/7/07, Paul Smith <phhs80_at_gmail.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
> > > > [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".
> >
> > Furthermore, X^2 is everywhere differentiable and notwithstanding the
> > reported problem occurs with
> >
> > myfunc <- function(x) {
> > x1 <- x[1]
> > x2 <- x[2]
> > (x1-x2)^2
> > }
> >
> > optim(c(0.2,0.2),myfunc,lower=c(0,0),upper=c(1,1),method="L-BFGS-B",control=
> > list(fnscale=-1))
> >
> > Paul
> >
> > ______________________________________________
> > R-help_at_stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
>

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