R help - Feb 2009 - optimal control, maximization with several variables?

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



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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

> 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
>  
>  
>  
>  -- 
>  Jetzt 1 Monat kostenlos! GMX FreeDSL - Telefonanschluss + DSL 
>  f?r nur 17,95 Euro/mtl.!* 
>  
>  ______________________________________________
>  R-help at r-project.org mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.