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))
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: apjaworski at mmm.com
Tel: (651) 733-6092
Fax: (651) 736-3122
"Paul Smith"
<phhs80 at gmail.com
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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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G'day Paul, On Mon, 7 May 2007 22:30:32 +0100 "Paul Smith" <phhs80 at gmail.com> 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
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" <phhs80 at gmail.com> 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)) ______________________________________________ R-help at 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. ******************************************************************* This email and any attachments are confidential. Any use, co...{{dropped}}