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.
