From: Duncan Murdoch <murdoch_at_stats.uwo.ca>

Date: Sun, 06 Jan 2008 20:04:06 -0500

*>>> 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
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*>> do it in R, you'd need to choose some finite dimensional parametrization
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*>> 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
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*>> the integral analytically or numerically to give your objective
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*>> function. Then there are some optimizers available, but in my
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*>> 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.
*

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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 - 01:08:12 GMT

Date: Sun, 06 Jan 2008 20:04:06 -0500

On 06/01/2008 7:55 PM, Paul Smith wrote:

> 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

> > 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.)

Linear splines are just piecewise linear functions. An easy way to parametrize them is by their value at a sequence of locations; they interpolate linearly between there.

x would be piecewise quadratic, so its integral would be a sum of cubic terms.

Duncan Murdoch

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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 - 01:08:12 GMT

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