On 06/01/2008 7:55 PM, Paul Smith wrote: > 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.)
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 ______________________________________________ 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.
