[R] optimal control, maximization with several variables?

[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



-- 
Jetzt 1 Monat kostenlos! GMX FreeDSL - Telefonanschluss + DSL 
für nur 17,95 Euro/mtl.!* http://dsl.gmx.de/?ac=OM.AD.PD003K11308T4569a