[R] Can R solve this optimization problem?

[Paul Smith]

On Jan 7, 2008 1:32 AM, Gabor Grothendieck <ggrothendieck at 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?

Paul