[R] Can R solve this optimization problem?

[Ravi Varadhan]

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.

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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

 

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-----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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