From: Gabor Grothendieck <ggrothendieck_at_gmail.com>

Date: Sun, 6 Jan 2008 21:22:12 -0500

R-help_at_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. Received on Mon 07 Jan 2008 - 02:25:35 GMT

Date: Sun, 6 Jan 2008 21:22:12 -0500

On Jan 6, 2008 8:43 PM, Paul Smith <phhs80_at_gmail.com> wrote:

*>
*

> On Jan 7, 2008 1:32 AM, Gabor Grothendieck <ggrothendieck@gmail.com> 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 <phhs80_at_gmail.com> 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?
*

If a linear approx is sufficient then yes; otherwise, no. For
example, if x can

be constrained to be small then its roughly true that sin(x) = x and you are
back to the original problem.

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