[R] Can R solve this optimization problem?

[Paul Smith]

Yes, Gabor, that is the interpretation that I meant. Thanks for the
clarification.

Paul


On Jan 7, 2008 5:59 PM, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
> 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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> > and provide commented, minimal, self-contained, reproducible code.
> >
> > ______________________________________________
> > 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.
> >
>