[R] Bad optimization solution

[S Ellison]

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))

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