[R] Can R solve this optimization problem?

[Paul Smith]

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