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 <[EMAIL PROTECTED]> 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: [EMAIL PROTECTED] > > Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html > > > > ---------------------------------------------------------------------------- > -------- > > > > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 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 > > ______________________________________________ > R-help@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. > > ______________________________________________ > R-help@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. > ______________________________________________ R-help@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.
