[R] optimal control, maximization with several variables?

Ravi Varadhan rvaradhan at jhmi.edu
Thu Feb 5 17:33:51 CET 2009

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.



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
>  -- 
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>  and provide commented, minimal, self-contained, reproducible code.

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