On Jan 7, 2008 1:04 AM, Duncan Murdoch <[EMAIL PROTECTED]> 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.) > > 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.
Thanks, Duncan, for your explanation. Paul ______________________________________________ R-help@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.
