On Jan 7, 2008 12:18 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.) 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.
