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optimal control, maximization with several variables?

2 messages · Frederik Noack, Ravi Varadhan

Frederik Noack
# 
Dear all,
I would like to solve the following problem, which can be done with optimal control theory or dynamic programming:

max(x,y) a*u1+b*u2+c*f1(u2)   s.t.  0<u1<x, 0<u2<f2(x,u2),  x'=f3(u1,u2,x)

which can be rewritten if optimal control theory should be applied as

H=a*u1+b*u2+c*f1(u2)+lambda*(x')             s.t. 0<u1<x, 0<u2<f2(x,u2)

The maximum principle conditions would solve the problem.
However in steady state conditions the system simplifies further with u1=x' und lambda=a.
Is it possible to solve this problem in R and if yes then how?
It might be sufficient for me to maximize a simple nonlinear function
f(x,y) w.r.t. x and y.
Does anyone know how to do it? I tried optim and genoud but untill now it did not work.
Best wishes
Frederik
Ravi Varadhan
# 
I assume that you are looking to solve, in R, the constrained optimization problem:

H (u1, u2) = a*u1+b*u2+c*f1(u2)+lambda*(x')             
with constraints: 0<u1<x, 0<u2<f2(x,u2)

where a, b, x, and x' are known.
 
Am I right?

If so, you can use the package Rdonlp2.  

I have written an extension of ConstrOptim that can handle nonlinear inequality constraints. This is another option.

Best,
Ravi.

____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: Frederik Noack <frederik.noack at gmx.de>
Date: Thursday, February 5, 2009 8:47 am
Subject: [R] optimal control, maximization with several variables?
To: R-help at r-project.org