[R] optimal control, maximization with several variables?
Frederik Noack
frederik.noack at gmx.de
Thu Feb 5 13:50:12 CET 2009
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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