[R] Can R solve this optimization problem?
Duncan Murdoch
murdoch at stats.uwo.ca
Mon Jan 7 01:18:51 CET 2008
On 06/01/2008 7:05 PM, Paul Smith wrote:
> Dear All,
>
> 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.
Duncan Murdoch
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