Re: [R] Bad optimization solution
Thanks, Ravi, for your clear explanation! Paul On 5/8/07, RAVI VARADHAN <[EMAIL PROTECTED]> wrote: > Paul, > > The problem lies neither with R nor with numercial methods. The onus is > always on the user to understand what the numerical schemes can do and what > they can't do. One should never blindly take the results given by a > numerical scheme and run with it. In your example, the optimization method > is doing what it was designed to do: to find a critical point of a function > where the gradient is zero. It is your responsibility to ensure that the > result makes sense, and if it doesn't, to understand why it doesn't make > sense. In your problem, maxima ((1,0) and (0,1)) lie on the boundary of the > parameter space, and the gradient at the maxima (defined as the limit from > within the domain) are clearly not zero. Another problem with your example > is that the hessian for your function is singular, it has eigenvalues of 0 > and 2. In short, there is no substitute to using your analytic powers! > > Ravi. > > - Original Message - > From: Paul Smith <[EMAIL PROTECTED]> > Date: Tuesday, May 8, 2007 4:33 am > Subject: Re: [R] Bad optimization solution > To: R-help > > > > 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 > > > > > > On 5/8/07, Ravi Varadhan <[EMAIL PROTECTED]> wrote: > > > 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. > > > > > > > > > > > --- > > > > > > Ravi Varadhan, Ph.D. > > > > > > 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 > > > > > > Email: [EMAIL PROTECTED] > > > > > > Webpage: > > > > > > > > > > > > > > > > > > > > > > > > > > -Original Message- > > > From: [EMAIL PROTECTED] > > > [ 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 <[EMAIL PROTECTED]> 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" > > > > > <[EMAIL PROTECTED] > > > > > > > > > To > > > > > Sent by: R-help > > > > > > > [EMAIL PROTECTED] > > > cc > > > > > at.math.ethz.ch > > > > > > > > Subject > > > > >[R] Bad optimization solution > > > > > 05/07/2007 04:30 > > > > > PM > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > Dear Al
Re: [R] Bad optimization solution
Paul,
You have picked a function that is not smoothly differentiable and also started
at one of many 'stationary' points in a system with multiple solutions. In
practice, I think it'll get a zero gradient as the algorithm does things
numerically and you have a symmetric function. It probably then chooses
gradient-related step sizes of zero and goes nowhere, converging instantly. The
same happens at (0.1,0.1) and anywhere else along x=y.
The problem affects pretty much all gradient-only algorithms handed stationary
points in a symmetric function.
Solution? Ermm.. "don't do that with a gradient method", I suspect, though
wiser heads may have more to say on the topic.
S
>>> "Paul Smith" <[EMAIL PROTECTED]> 07/05/2007 22:30:32 >>>
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))
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Re: [R] Bad optimization solution
Paul,
The problem lies neither with R nor with numercial methods. The onus is always
on the user to understand what the numerical schemes can do and what they can't
do. One should never blindly take the results given by a numerical scheme and
run with it. In your example, the optimization method is doing what it was
designed to do: to find a critical point of a function where the gradient is
zero. It is your responsibility to ensure that the result makes sense, and if
it doesn't, to understand why it doesn't make sense. In your problem, maxima
((1,0) and (0,1)) lie on the boundary of the parameter space, and the gradient
at the maxima (defined as the limit from within the domain) are clearly not
zero. Another problem with your example is that the hessian for your function
is singular, it has eigenvalues of 0 and 2. In short, there is no substitute
to using your analytic powers!
Ravi.
- Original Message -
From: Paul Smith <[EMAIL PROTECTED]>
Date: Tuesday, May 8, 2007 4:33 am
Subject: Re: [R] Bad optimization solution
To: R-help
> 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
>
>
> On 5/8/07, Ravi Varadhan <[EMAIL PROTECTED]> wrote:
> > 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.
> >
> >
>
> > ---
> >
> > Ravi Varadhan, Ph.D.
> >
> > 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
> >
> > Email: [EMAIL PROTECTED]
> >
> > Webpage:
> >
> >
> >
> >
> ----
> >
> >
> >
> > -Original Message-
> > From: [EMAIL PROTECTED]
> > [ 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 <[EMAIL PROTECTED]> 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"
> > > > <[EMAIL PROTECTED]
> > > > >
> > To
> > > > Sent by: R-help
>
> > > > [EMAIL PROTECTED]
> > 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]
> > >
Re: [R] Bad optimization solution
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
>
>
> On 5/8/07, Ravi Varadhan <[EMAIL PROTECTED]> wrote:
> > 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.
> >
> >
> > ---
> >
> > Ravi Varadhan, Ph.D.
> >
> > 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
> >
> > Email: [EMAIL PROTECTED]
> >
> > Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
> >
> >
> >
> > ------------
> >
> >
> >
> > -Original Message-
> > From: [EMAIL PROTECTED]
> > [mailto:[EMAIL PROTECTED] 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 <[EMAIL PROTECTED]> 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"
> > > > <[EMAIL PROTECTED]
> > > > >
> > To
> > > > Sent by: R-help
> > > >
> > > > [EMAIL PROTECTED]
> > 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).
> > > >
> > &
Re: [R] Bad optimization solution
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
On 5/8/07, Ravi Varadhan <[EMAIL PROTECTED]> wrote:
> 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.
>
>
> ---
>
> Ravi Varadhan, Ph.D.
>
> 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
>
> Email: [EMAIL PROTECTED]
>
> Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
>
>
>
>
> -Original Message-
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] 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 <[EMAIL PROTECTED]> 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"
> > > <[EMAIL PROTECTED]
> > > >
> To
> > > Sent by: R-help
> > > [EMAIL PROTECTED]
> 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@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
__
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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Re: [R] Bad optimization solution
G'day all, On Tue, 8 May 2007 12:10:25 +0800 Berwin A Turlach <[EMAIL PROTECTED]> wrote: > > I am trying to perform the below optimization problem, but getting > > (0.5,0.5) as optimal solution, which is wrong; > > Why? > > As far as I can tell you are trying to minimize |x1-x2| It was pointed out to me that you are actually trying to maximise the function, sorry, didn't read the command carefully enough. And I also noticed that my comments were anyhow wrong, for minimisation the points (x,x) and not (x, 1-x) would be the solutions; must have also misread the function as |x1+x2|... Looks as if I need more coffee to wake up and get my brain going... Please ignore my last two mails on this issue and apologise to the list Cheers, Berwin __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Bad optimization solution
G'day Paul,
On Mon, 7 May 2007 23:25:52 +0100
"Paul Smith" <[EMAIL PROTECTED]> wrote:
[...]
> 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
> }
Same argument as with abs(x1-x2) holds. (x1-x2)^2 is non-negative for
all x1, x2. All points of the form (x, 1-x) where x is between 0 and 1
satisfy the constraints and achieve a function value of 0. Hence, all
such points are solutions.
There is no problem. Except if there are further constraints that
reduce the set of possible solutions which you have not told us about.
Cheers,
Berwin
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Re: [R] Bad optimization solution
G'day Paul, On Mon, 7 May 2007 22:30:32 +0100 "Paul Smith" <[EMAIL PROTECTED]> wrote: > I am trying to perform the below optimization problem, but getting > (0.5,0.5) as optimal solution, which is wrong; Why? As far as I can tell you are trying to minimize |x1-x2| where x1 and x2 are between 0 and 1. The minimal value that the absolute function can take is zero and any point (x1,x2)=(x,1-x) where x is between 0 and 1 will achieve this value and also respect the constraints that you have imposed. Hence, any such point, including (0.5,0.5) is a solution to your problem. > the correct solution should be (1,0) or (0,1). Why? Unless there are some additional constraint that you have not told optim() (and us) about, these are two possible solutions from an infinite set of solutions. As I said, any point of the form (x, 1-x) with x between 0 and 1 is a solution to your problem, unless I am missing something Cheers, Berwin __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Bad optimization solution
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.
---
Ravi Varadhan, Ph.D.
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
Email: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] 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 <[EMAIL PROTECTED]> 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"
> > <[EMAIL PROTECTED]
> > >
To
> > Sent by: R-help
> > [EMAIL PROTECTED]
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
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Re: [R] Bad optimization solution
Paul Smith said the following on 5/7/2007 3:25 PM:
> On 5/7/07, Paul Smith <[EMAIL PROTECTED]> 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"
>>> <[EMAIL PROTECTED]
>>> > To
>>> Sent by: R-help
>>> [EMAIL PROTECTED] 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
>
Then perhaps supply the gradient:
mygrad <- function(x) {
x1 <- x[1]
x2 <- x[2]
c(2, -2) * c(x1, x2)
}
optim(c(0.2,0.2),myfunc,mygrad,lower=c(0,0),upper=c(1,1),
method="L-BFGS-B",control=list(fnscale=-1))
HTH,
--sundar
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Re: [R] Bad optimization solution
On 5/7/07, Paul Smith <[EMAIL PROTECTED]> 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"
> > <[EMAIL PROTECTED]
> > > To
> > Sent by: R-help
> > [EMAIL PROTECTED] 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
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Re: [R] Bad optimization solution
On 5/7/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> 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"
> <[EMAIL PROTECTED]
> > To
> Sent by: R-help
> [EMAIL PROTECTED] 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".
Paul
__
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Re: [R] Bad optimization solution
Paul,
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.
Andy
__
Andy Jaworski
518-1-01
Process Laboratory
3M Corporate Research Laboratory
-
E-mail: [EMAIL PROTECTED]
Tel: (651) 733-6092
Fax: (651) 736-3122
"Paul Smith"
<[EMAIL PROTECTED]
> To
Sent by: R-help
[EMAIL PROTECTED] 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))
__
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PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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R-help@stat.math.ethz.ch mailing list
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[R] Bad optimization solution
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))
__
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and provide commented, minimal, self-contained, reproducible code.
