On Jan 7, 2008 1:32 AM, Gabor Grothendieck <[EMAIL PROTECTED]> wrote: > This can be discretized to a linear programming problem > so you can solve it with the lpSolve package. Suppose > we have x0, x1, x2, ..., xn. Our objective (up to a > multiple which does not matter) is: > > Maximize: x1 + ... + xn > > which is subject to the constraints: > > -1/n <= x1 - x0 <= 1/n > -1/n <= x2 - x1 <= 1/n > ... > -1/n <= xn - x[n-1] <= 1/n > and > x0 = xn = 0 > > > On Jan 6, 2008 7:05 PM, Paul Smith <[EMAIL PROTECTED]> 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.
Thats is clever, Gabor! But suppose that the objective function is integral of sin( x( t ) ) with t from 0 to 1 and consider the same constraints. Can your method be adapted to get the solution? 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.
