# [R] Can R solve this optimization problem?

Gabor Grothendieck ggrothendieck at gmail.com
Mon Jan 7 02:32:31 CET 2008

```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.
>
>
> Paul
>
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