[R] Can R solve this optimization problem?

[Gabor Grothendieck]

I think what he meant is that x is a function of t so if dx/dt is regarded
to be a function of t, which we shall call u(t), then u(t)'s absolute value
at each value of t is less than or equal to 1 (as opposed to u(t) being
known).

On Jan 7, 2008 11:32 AM, Ravi Varadhan <rvaradhan at jhmi.edu> wrote:
> Hi Paul,
>
> Your problem statement does not make much sense to me.  You say that an
> analytical solution can be found easily.  I don't see how.
>
> This is a variational calculus type problem, where you maximize a
> functional.  Your constraint dx/dt=u(t) means that there exists a solution
> (the anti-derivative of u) that is unique up to an arbitrary constant.
> However, a solution may not even exist since you are imposing two conditions
> on it: x(0) = x(1) = 0.  If your solution satisfies both conditions, then it
> certainly is unique, and it is the x(t) that maximizes integral.
>
> Ravi.
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
> ----------------------------------------------------------------------------
> --------
>
>
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of Paul Smith
> Sent: Sunday, January 06, 2008 7:06 PM
> To: r-help
> Subject: [R] Can R solve this optimization problem?
>
> 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.
>
> Thanks in advance,
>
> Paul
>
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