From: Paul Smith <phhs80_at_gmail.com>

Date: Mon, 7 Jan 2008 00:55:26 +0000

R-help_at_r-project.org 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. Received on Mon 07 Jan 2008 - 01:02:16 GMT

Date: Mon, 7 Jan 2008 00:55:26 +0000

On Jan 7, 2008 12:18 AM, Duncan Murdoch <murdoch_at_stats.uwo.ca> wrote:

> > I am trying to solve the following maximization problem with R:

*> >
**> > find x(t) (continuous) that maximizes the
**> >
**> > integral of x(t) with t from 0 to 1,
**> >
**> > subject to the constraints
**> >
**> > dx/dt = u,
**> >
**> > |u| <= 1,
**> >
**> > x(0) = x(1) = 0.
**> >
**> > The analytical solution can be obtained easily, but I am trying to
**> > understand whether R is able to solve numerically problems like this
**> > one. I have tried to find an approximate solution through
**> > discretization of the objective function but with no success so far.
**>
**> R doesn't provide any way to do this directly. If you really wanted to
**> do it in R, you'd need to choose some finite dimensional parametrization
**> of u (e.g. as a polynomial or spline, but the constraint on it would
**> make the choice tricky: maybe a linear spline?), then either evaluate
**> the integral analytically or numerically to give your objective
**> function. Then there are some optimizers available, but in my
**> experience they aren't very good on high dimensional problems: so your
**> solution would likely be quite crude.
**>
**> I'd guess you'd be better off in Matlab, Octave, Maple or Mathematica
**> with a problem like this.
*

Thanks, Duncan. I have placed a similar post in the Maxima list and another one in the Octave list. (I have never used splines; so I did not quite understand the method that you suggested to me.)

Paul

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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. Received on Mon 07 Jan 2008 - 01:02:16 GMT

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