Can R solve this optimization problem?
On Jan 6, 2008 8:43 PM, Paul Smith <phhs80 at gmail.com> wrote:
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?
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.