[R] Optimization

[Prof Brian Ripley]

>From the help page:

Note:

      'optim' will work with one-dimensional 'par's, but the default
      method does not work well (and will warn).  Use 'optimize'
      instead.

Next, there is a constraint of x>=0 that you are not imposing.

Finally, it is easy to see that qnorm(0.7, 0.0032, x) is monotome in x, so 
the solution is x=0.  In fact, x1 = 0.0032 + sqrt(x) * qnorm(0.7).

optim(0.0207, fr)  does a good enough job, as does
optimize(fr, low=0, up=0.05)


Advice: numerical optimization is not a black box, and has to be used with 
some analysis of the problem to hand.  See e.g. MASS4, chapter 16.


On Mon, 18 Jun 2007, livia wrote:

>
> Hi, I would like to minimize the value of x1-x2, x2 is a fixed value of 0.01,
> x1 is the quantile of normal distribution (0.0032,x) with probability of
> 0.7, and the changing value should be x. Initial value for x is 0.0207. I am
> using the following codes, but it does not work.
>
> fr <- function(x) {
>      x1<-qnorm(0.7,0.0032,x)
>      x2=0.01
>      x1-x2
> }
> xsd <- optim(0.0207, fr, NULL,method="BFGS")
>
> It is the first time I am trying to use optimization. Could anyone give me
> some advice?
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595